A132290 -id:A132290

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A132289

Triangle, read by rows of 2n+1 terms, where T(n,k) = T(n,k-1) + T(n-1,k-1) for 2n>=k>0, T(n,2n-1) = T(n,2n-2) + T(n-1,n-1) and T(n,2n) = T(n,2n-1) + T(n-1,n-1) for n>0, with T(n,0) = T(n-1,n-1) for n>0 and T(0,0) = 1.

+10
1

1, 1, 2, 3, 3, 4, 6, 9, 12, 12, 15, 19, 25, 34, 46, 58, 58, 70, 85, 104, 129, 163, 209, 267, 325, 325, 383, 453, 538, 642, 771, 934, 1143, 1410, 1735, 2060, 2060, 2385, 2768, 3221, 3759, 4401, 5172, 6106, 7249, 8659, 10394, 12454, 14514, 14514, 16574, 18959

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

Column 0 and the rightmost border (shifted right) equal A125276.

LINKS

Table of n, a(n) for n=0..51.

EXAMPLE

Triangle begins:

1, 2, 3;

3, 4, 6, 9, 12;

12, 15, 19, 25, 34, 46, 58;

58, 70, 85, 104, 129, 163, 209, 267, 325;

325, 383, 453, 538, 642, 771, 934, 1143, 1410, 1735, 2060;

2060, 2385, 2768, 3221, 3759, 4401, 5172, 6106, 7249, 8659, 10394, 12454, 14514; ...

PROG

(PARI) T(n, k)=my(A=[1]); if(2*n<k || k<0, 0, if(n==0, 1, for(i=1, n, A=Vec(Ser(concat(concat(A[ #A], A), A[ #A]))/(1-x))); A[k+1]))

CROSSREFS

Cf. A132290 (main diagonal), A125276 (column 0).

KEYWORD

nonn,tabf,changed

AUTHOR

Paul D. Hanna, Aug 18 2007

STATUS

approved

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