Boustrophedon transform: Difference between revisions
Added Sidef
(→{{header|Perl}}: use vecsum from ntheory (~4x faster) (Math::AnyNum::sum() would be even faster)) |
(Added Sidef) |
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Line 976:
1 2 5 17 73 381 2347 16701 134993 1222873 12279251 135425553 1627809401 21183890469 296773827547
1000th term: 13714256926920345740…19230014799151339821 (2566 digits)</pre>
=={{header|Sidef}}==
<syntaxhighlight lang="ruby">func boustrophedon_transform(seq) {
func T(k,n) is cached {
return seq[k] if (n == 0)
T(k, n-1) + T(k-1, k-n)
}
var bt = seq.range.map {|n| T(n,n) }
T.uncache
return bt
}
const N = 100 # n terms
[
'1 followed by 0\'s A000111', Math.seq(1,{0}),
'All-1\'s A000667', Math.seq({1}),
'(-1)^n A062162', Math.seq({|_,k| (-1)**(k+1) }),
'Primes A000747', Math.seq(2,{ .tail.next_prime }),
'Fibbonaccis A000744', Math.seq(1,1,{ .last(2).sum }),
'Factorials A230960', Math.seq(1,{|a,k| a.last * (k-1) }),
].each_slice(2, {|name, seq|
var bt = boustrophedon_transform(seq.first(N))
say "\n#{name}:\n#{bt.first(15).join(' ')}"
var v = bt[N-1]
say ("#{N}th term: ", Str(v).first(20), '..', Str(v).last(20), " (%s digits)" % v.len)
})</syntaxhighlight>
{{out}}
<pre>
1 followed by 0's A000111:
1 1 1 2 5 16 61 272 1385 7936 50521 353792 2702765 22368256 199360981
100th term: 45608516616801111821..68991870306963423232 (137 digits)
All-1's A000667:
1 2 4 9 24 77 294 1309 6664 38177 243034 1701909 13001604 107601977 959021574
100th term: 21939873756450413339..30507739683220525509 (138 digits)
(-1)^n A062162:
1 0 0 1 0 5 10 61 280 1665 10470 73621 561660 4650425 41441530
100th term: 94810791122872999361..65519440121851711941 (136 digits)
Primes A000747:
2 5 13 35 103 345 1325 5911 30067 172237 1096319 7677155 58648421 485377457 4326008691
100th term: 98967625721691921699..78027927576425134967 (138 digits)
Fibbonaccis A000744:
1 2 5 14 42 144 563 2526 12877 73778 469616 3288428 25121097 207902202 1852961189
100th term: 42390820205259437020..42168748587048986542 (138 digits)
Factorials A230960:
1 2 5 17 73 381 2347 16701 134993 1222873 12279251 135425553 1627809401 21183890469 296773827547
100th term: 31807659526053444023..65546706672657314921 (157 digits)
</pre>
=={{header|Wren}}==
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