A113993 Triangle, read by rows, where column k equals column 0 of A113983^(k+1): T(n,k) = [A113983^(k+1)](n-k,0) for n>=k>=0.

1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 8, 9, 4, 1, 1, 18, 27, 16, 5, 1, 1, 46, 89, 64, 25, 6, 1, 1, 136, 327, 276, 125, 36, 7, 1, 1, 464, 1353, 1304, 665, 216, 49, 8, 1, 1, 1818, 6303, 6808, 3825, 1366, 343, 64, 9, 1, 1, 8122, 32953, 39320, 23977, 9246, 2513, 512, 81, 10, 1

Offset

0,5

Links

Table of n, a(n) for n=0..65.

Formula

T(n, k) = A113983(n+1, k) - T(n, k-1).

Example

Triangle T begins:
1;
1,1;
1,2,1;
1,4,3,1;
1,8,9,4,1;
1,18,27,16,5,1;
1,46,89,64,25,6,1;
1,136,327,276,125,36,7,1;
1,464,1353,1304,665,216,49,8,1;
1,1818,6303,6808,3825,1366,343,64,9,1;
1,8122,32953,39320,23977,9246,2513,512,81,10,1; ...
where A113983(n+1,k) = T(n,k) + T(n,k-1):
A113983(6,3) = 43 = T(5,3) + T(5,2) = 16 + 27;
A113983(7,3) = 153 = T(6,3) + T(6,2) = 64 + 89;
A113983(8,3) = 603 = T(7,3) + T(7,2) = 276 + 327.

Prog

(PARI) T(n, k)=local(A, B); A=Mat(1); for(m=2, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(i<3 || j==1 || j==i, B[i, j]=1, B[i, j]=A[i-1, j-1]+(A^2)[i-2, j-1] ); )); A=B); (A^(k+1))[n-k+1, 1]

Crossrefs

Cf. A113983, A113988, A113989 (column 1), A113994 (column 2), A113995 (column 3), A113996 (column 4), A113997 (row sums).

Sequence in context: A167630 A322264 A009998 * A103323 A329332 A092056

Adjacent sequences: A113990 A113991 A113992 * A113994 A113995 A113996

Keyword

nonn,tabl

Author

Paul D. Hanna, Nov 12 2005

Status

approved