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A288267
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Triangle read by rows: T(n,k) = T(n,k+1) + T(n-k,k-1) with T(0,0) = 1 and T(n,k) = 0 if k<0 or k > A003056(n).
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3
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1, 1, 1, 1, 1, 2, 2, 1, 3, 3, 1, 5, 5, 2, 9, 9, 4, 1, 15, 15, 6, 1, 26, 26, 11, 2, 45, 45, 19, 4, 78, 78, 33, 7, 1, 135, 135, 57, 12, 1, 234, 234, 99, 21, 2, 406, 406, 172, 37, 4, 704, 704, 298, 64, 7, 1222, 1222, 518, 112, 13, 1, 2120, 2120, 898, 194, 22, 1, 3679
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OFFSET
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0,6
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LINKS
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EXAMPLE
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First few rows are:
1;
1, 1;
1, 1;
2, 2, 1;
3, 3, 1;
5, 5, 2;
9, 9, 4, 1;
15, 15, 6, 1.
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MAPLE
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T:= proc(n, k) option remember; `if`(k<0 or k*(k+1)/2>n, 0,
`if`(n=0, 1, T(n, k+1)+T(n-k, k-1)))
end:
seq(seq(T(n, k), k=0..floor((sqrt(1+8*n)-1)/2)), n=0..20); # Alois P. Heinz, Sep 01 2017
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MATHEMATICA
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T[n_, k_] := T[n, k] = If[k < 0 || k(k+1)/2 > n, 0, If[n == 0, 1, T[n, k+1] + T[n-k, k-1]]];
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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