A185624 Triangle, read by rows, equal to the matrix square of triangle A185620.

1, 2, 1, 3, 2, 1, 6, 7, 2, 1, 18, 28, 11, 2, 1, 79, 142, 66, 15, 2, 1, 463, 913, 470, 120, 19, 2, 1, 3396, 7244, 3997, 1098, 190, 23, 2, 1, 30073, 69004, 40079, 11587, 2122, 276, 27, 2, 1, 314037, 771359, 466448, 140092, 26707, 3638, 378, 31, 2, 1, 3796561, 9933242, 6208551, 1921122

Offset

0,2

Links

Table of n, a(n) for n=0..58.

Example

 Triangle begins:
1;
2, 1;
3, 2, 1;
6, 7, 2, 1;
18, 28, 11, 2, 1;
79, 142, 66, 15, 2, 1;
463, 913, 470, 120, 19, 2, 1;
3396, 7244, 3997, 1098, 190, 23, 2, 1;
30073, 69004, 40079, 11587, 2122, 276, 27, 2, 1;
314037, 771359, 466448, 140092, 26707, 3638, 378, 31, 2, 1;
3796561, 9933242, 6208551, 1921122, 377495, 53149, 5742, 496, 35, 2, 1; ...
This triangle equals the matrix square, R^2, 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^2)[n+1, k+1])}

Crossrefs

Cf. A185620, A185625, A185626, A185627, A185628.

Sequence in context: A054098 A132089 A321155 * A162387 A107880 A102228

Adjacent sequences: A185621 A185622 A185623 * A185625 A185626 A185627

Keyword

nonn,tabl

Author

Paul D. Hanna, Sep 07 2011

Status

approved