A185628 Triangle, read by rows, equal to the matrix cube of triangle A185620.

1, 3, 1, 6, 3, 1, 16, 12, 3, 1, 60, 55, 18, 3, 1, 305, 315, 118, 24, 3, 1, 1988, 2243, 912, 205, 30, 3, 1, 15951, 19378, 8342, 1995, 316, 36, 3, 1, 153171, 198363, 89193, 22274, 3708, 451, 42, 3, 1, 1722693, 2358860, 1098552, 283427, 48863, 6195, 610, 48, 3, 1, 22296396, 32060736

Offset

0,2

Links

Table of n, a(n) for n=0..56.

Example

 Triangle begins:
1;
3, 1;
6, 3, 1;
16, 12, 3, 1;
60, 55, 18, 3, 1;
305, 315, 118, 24, 3, 1;
1988, 2243, 912, 205, 30, 3, 1;
15951, 19378, 8342, 1995, 316, 36, 3, 1;
153171, 198363, 89193, 22274, 3708, 451, 42, 3, 1;
1722693, 2358860, 1098552, 283427, 48863, 6195, 610, 48, 3, 1;
22296396, 32060736, 15376126, 4070883, 720586, 94085, 9600, 793, 54, 3, 1; ...
This triangle equals the matrix cube, R^3, of triangle R = A185620, which begins:
1;
1, 1;
1, 1, 1;
1, 3, 1, 1;
1, 10, 5, 1, 1;
1, 42, 27, 7, 1, 1;
1, 226, 173, 52, 9, 1, 1;
1, 1525, 1330, 442, 85, 11, 1, 1;
1, 12555, 12134, 4345, 897, 126, 13, 1, 1; ...
where R^3 - R^2 + I equals R shifted left one column.

Prog

 (PARI) {T(n, k)=local(A=Mat(1), B); for(m=1, n, B=A^3-A^2+A^0; A=matrix(m+1, m+1); for(i=1, m+1, for(j=1, i, if(i<2|j==i, A[i, j]=1, if(j==1, A[i, j]=1, A[i, j]=B[i-1, j-1]))))); return((A^3)[n+1, k+1])}

Crossrefs

Cf. A185620, A185624, A185629, A185630, A185631.

Sequence in context: A039805 A094504 A107884 * A321194 A158822 A353924

Adjacent sequences: A185625 A185626 A185627 * A185629 A185630 A185631

Keyword

nonn,tabl

Author

Paul D. Hanna, Sep 07 2011

Status

approved