A113995 Column 3 of triangle A113993, also equals column 0 of A113983^4.

1, 4, 16, 64, 276, 1304, 6808, 39320, 250752, 1759604, 13530928, 113522192, 1034613180, 10199679712, 108334569184, 1235056156832, 15059906315120, 195775382409972, 2705084927865600, 39616257445460560, 613348477806011476

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Example

A113983^4, the matrix 4th power of triangle A113983, begins:
1;
4,1;
16,8,1;
64,48,12,1;
276,272,100,16,1;
1304,1576,752,172,20,1;
6808,9664,5592,1624,264,24,1;
39320,63696,42848,14828,3008,376,28,1;
250752,454192,345200,136888,32628,5024,508,32,1; ...

Prog

(PARI) a(n)=local(A, B); A=Mat(1); for(m=2, n+2, 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^4)[n+1, 1]

Crossrefs

Cf. A113993, A113989 (column 1), A113994 (column 2), A113996 (column 4), A113997 (row sums); A113983.

Sequence in context: A270560 A071357 A142872 * A212443 A294036 A097679

Adjacent sequences: A113992 A113993 A113994 * A113996 A113997 A113998

Keyword

nonn

Author

Paul D. Hanna, Nov 12 2005

Status

approved