A113716 Triangle, read by rows, where row n forms a polynomial in y=3*k that generates diagonal n as k=0,1,2,... for n>=0; thus T(n,k) = Sum_{j=0..n-k} T(n-k,j)*(3*k)^j, with T(n,0)=T(n,n)=1.

1, 1, 1, 1, 4, 1, 1, 22, 7, 1, 1, 157, 61, 10, 1, 1, 1372, 601, 118, 13, 1, 1, 14008, 6595, 1495, 193, 16, 1, 1, 161995, 79981, 20206, 3001, 286, 19, 1, 1, 2079994, 1065589, 291394, 48685, 5281, 397, 22, 1, 1, 29268778, 15495415, 4492621, 825313, 100456

Offset

0,5

Links

Table of n, a(n) for n=0..50.

Example

Triangle begins:
1;
1,1;
1,4,1;
1,22,7,1;
1,157,61,10,1;
1,1372,601,118,13,1;
1,14008,6595,1495,193,16,1;
1,161995,79981,20206,3001,286,19,1;
1,2079994,1065589,291394,48685,5281,397,22,1;
1,29268778,15495415,4492621,825313,100456,8497,526,25,1; ...
where diagonals are generated by row polynomials:
T(6,5) = (1) + (1)*(3*5) = 16.
T(6,4) = (1) + (4)*(3*4) + (1)*(3*4)^2 = 193.
T(6,3) = (1) + (22)*(3*3) + (7)*(3*3)^2 + (1)*(3*3)^3 = 1495.
T(6,2) = (1) + (157)*(3*2) + (61)*(3*2)^2 + (10)*(3*2)^3 + (1)*(3*2)^4 = 6595.

Prog

(PARI) T(n, k)=if(n<k || k<0, 0, if(n==k || k==0, 1, sum(j=0, n-k, T(n-k, j)*(3*k)^j)))

Crossrefs

Cf. A091150, A113711, A113717 (column 1), A113718 (column 2), A113719 (row sums).

Sequence in context: A185946 A015113 A016519 * A220652 A169654 A357744

Adjacent sequences: A113713 A113714 A113715 * A113717 A113718 A113719

Keyword

nonn,tabl

Author

Paul D. Hanna, Nov 08 2005

Status

approved