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

Author

Paul D. Hanna, May 26 2007

Keywords

• nonn
• tabf

Examples

			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; ...
		

Crossrefs

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

Programs

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])}