A130457 Triangle, read by rows of 3n+1 terms, where row n+1 is generated by taking partial sums of row n and then appending 2 zeros followed by the final term in the partial sums of row n, for n>=0, with T(0,0)=1.

1, 1, 0, 0, 1, 1, 1, 1, 2, 0, 0, 2, 1, 2, 3, 5, 5, 5, 7, 0, 0, 7, 1, 3, 6, 11, 16, 21, 28, 28, 28, 35, 0, 0, 35, 1, 4, 10, 21, 37, 58, 86, 114, 142, 177, 177, 177, 212, 0, 0, 212, 1, 5, 15, 36, 73, 131, 217, 331, 473, 650, 827, 1004, 1216, 1216, 1216, 1428, 0, 0, 1428, 1, 6, 21, 57

Offset

0,9

Links

Table of n, a(n) for n=0..73.

Example

Triangle begins:
.1;
.1, 0, 0, 1;
.1, 1, 1, 2, 0, 0, 2;
.1, 2, 3, 5, 5, 5, 7, 0, 0, 7;
.1, 3, 6, 11, 16, 21, 28, 28, 28, 35, 0, 0, 35;
.1, 4, 10, 21, 37, 58, 86, 114, 142, 177, 177, 177, 212, 0, 0, 212;
.1, 5, 15, 36, 73, 131, 217, 331, 473, 650, 827, 1004, 1216, 1216, 1216, 1428, 0, 0, 1428; ...

Prog

(PARI) {T(n, k)=local(A=[1], B); if(n==0, if(k==0, 1, 0), for(j=1, n, B=Vec(Ser(A)/(1-x)); A=concat(concat(B, [0, 0]), B[ #B])); A[k+1])}

Crossrefs

Cf. A130458 (final term in rows); A130456 (variant).

Sequence in context: A281452 A341023 A241067 * A130454 A070787 A033985

Adjacent sequences: A130454 A130455 A130456 * A130458 A130459 A130460

Keyword

nonn,tabf

Author

Paul D. Hanna, May 26 2007

Status

approved