Motzkin numbers: Difference between revisions
Added Sidef
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40 66,368,199,913,921,497 false
41 192,137,918,101,841,817 false
</pre>
=={{header|Sidef}}==
Built-in:
<lang ruby>say 50.of { .motzkin }</lang>
Motzkin's triangle (the Motzkin numbers are on the hypotenuse of the triangle):
<lang ruby>func motzkin_triangle(num, callback) {
var row = []
{ |n|
row = [0, 1, {|i| row[i+2] + row[i] + row[i+1] }.map(0 .. n-3)..., 0]
callback(row.grep{ .> 0 })
} << 2..(num+1)
}
motzkin_triangle(10, {|row|
row.map { "%4s" % _ }.join(' ').say
})</lang>
{{out}}
<pre>
1
1 1
1 2 2
1 3 5 4
1 4 9 12 9
1 5 14 25 30 21
1 6 20 44 69 76 51
1 7 27 70 133 189 196 127
1 8 35 104 230 392 518 512 323
1 9 44 147 369 726 1140 1422 1353 835
</pre>
Task:
<lang ruby>func motzkin_numbers(N) {
var (a, b, n) = (0, 1, 1)
N.of {
var M = b//n #/
n += 1
(a, b) = (b, (3*(n-1)*n*a + (2*n - 1)*n*b) // ((n+1)*(n-1))) #/
M
}
}
motzkin_numbers(42).each_kv {|k,v|
say "#{'%2d' % k}: #{v}#{v.is_prime ? ' prime' : ''}"
}</lang>
{{out}}
<pre>
0: 1
1: 1
2: 2 prime
3: 4
4: 9
5: 21
6: 51
7: 127 prime
8: 323
9: 835
10: 2188
11: 5798
12: 15511 prime
13: 41835
14: 113634
15: 310572
16: 853467
17: 2356779
18: 6536382
19: 18199284
20: 50852019
21: 142547559
22: 400763223
23: 1129760415
24: 3192727797
25: 9043402501
26: 25669818476
27: 73007772802
28: 208023278209
29: 593742784829
30: 1697385471211
31: 4859761676391
32: 13933569346707
33: 40002464776083
34: 114988706524270
35: 330931069469828
36: 953467954114363 prime
37: 2750016719520991
38: 7939655757745265
39: 22944749046030949
40: 66368199913921497
41: 192137918101841817
</pre>
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