login
A185628
Triangle, read by rows, equal to the matrix cube of triangle A185620.
8
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
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
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Sep 07 2011
STATUS
approved