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.

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

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;
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)=local(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).

Sequence in context: A046936 A187067 A017831 * A078467 A154217 A361644

Adjacent sequences: A132286 A132287 A132288 * A132290 A132291 A132292

Keyword

nonn,tabf

Author

Paul D. Hanna, Aug 18 2007

Status

approved