Fibonacci sequence: Difference between revisions
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m (→{{header|Phix}}: added syntax colouring the hard way) |
(→Excel LAMBDA: Added a variant, obtaining just the Nth term, defined in terms of a fold.) |
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Or as a fold, obtaining just the Nth term of the Fibonacci series: |
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<lang lisp>FIBONACCI2 |
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=LAMBDA(n, |
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INDEX( |
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FOLDL( |
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LAMBDA(ab, |
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LAMBDA(_, |
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APPEND(INDEX(ab, 2))(SUM(ab)) |
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) |
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) |
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)({0;1})( |
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ENUMFROMTO(1)(n) |
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), |
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1 |
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) |
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)</lang> |
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Assuming the following generic bindings in the Excel worksheet Name manager: |
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<lang lisp>APPEND |
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=LAMBDA(xs, |
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LAMBDA(ys, |
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LET( |
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nx, ROWS(xs), |
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rowIndexes, SEQUENCE(nx + ROWS(ys)), |
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colIndexes, SEQUENCE( |
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1, |
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MAX(COLUMNS(xs), COLUMNS(ys)) |
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), |
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IF( |
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rowIndexes <= nx, |
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INDEX(xs, rowIndexes, colIndexes), |
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INDEX(ys, rowIndexes - nx, colIndexes) |
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) |
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) |
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) |
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) |
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ENUMFROMTO |
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=LAMBDA(a, |
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LAMBDA(z, |
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SEQUENCE(1 + z - a, 1, a, 1) |
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) |
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) |
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FOLDL |
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=LAMBDA(op, |
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LAMBDA(a, |
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LAMBDA(xs, |
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IF( |
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2 > ROWS(xs), |
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op(a)(xs), |
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FOLDL(op)( |
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op(a)( |
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HEAD(xs) |
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) |
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)( |
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TAIL(xs) |
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) |
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) |
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) |
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) |
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) |
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HEAD |
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=LAMBDA(xs, |
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INDEX(xs, 1, SEQUENCE(1, COLUMNS(xs))) |
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) |
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TAIL |
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=LAMBDA(xs, |
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INDEX( |
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xs, |
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SEQUENCE(ROWS(xs) - 1, 1, 2, 1), |
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SEQUENCE(1, COLUMNS(xs)) |
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) |
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)</lang> |
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{{Out}} |
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{| class="wikitable" |
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|- |
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|||style="text-align:right; font-family:serif; font-style:italic; font-size:120%;"|fx |
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! colspan="2" style="text-align:left; font-family:Arial, Helvetica, sans-serif !important;"|=FIBONACCI2(32) |
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|- style="text-align:center; font-family:Arial, Helvetica, sans-serif !important; background-color:#000000; color:#ffffff;" |
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| |
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| A |
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| B |
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|- style="text-align:center;" |
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| style="text-align:center; font-family:Arial, Helvetica, sans-serif !important; background-color:#000000; color:#ffffff" | 1 |
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| style="text-align:right; font-weight:bold" | |
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| Fibonacci |
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|- style="text-align:center;" |
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| style="text-align:center; font-family:Arial, Helvetica, sans-serif !important; background-color:#000000; color:#ffffff" | 2 |
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| style="text-align:right; font-weight:bold" | N=32 |
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| style="background-color:#cbcefb;" | 2178309 |
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|} |
|} |
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