A130528 Triangle T, read by rows, where row n+1 of T equals row n of matrix power T^n added to row n of T (shifted right).

1, 1, 1, 2, 2, 1, 12, 8, 3, 1, 156, 80, 20, 4, 1, 3540, 1516, 300, 40, 5, 1, 123400, 46236, 7816, 840, 70, 6, 1, 6091988, 2054980, 309268, 28816, 1960, 112, 7, 1, 402900176, 124679524, 17129124, 1437476, 85656, 4032, 168, 8, 1, 34289884368, 9862677332

Offset

0,4

Links

Table of n, a(n) for n=0..46.

Example

Triangle begins:
1;
1, 1;
2, 2, 1;
12, 8, 3, 1;
156, 80, 20, 4, 1;
3540, 1516, 300, 40, 5, 1;
123400, 46236, 7816, 840, 70, 6, 1;
6091988, 2054980, 309268, 28816, 1960, 112, 7, 1;
402900176, 124679524, 17129124, 1437476, 85656, 4032, 168, 8, 1; ...
Matrix square T^2 begins:
1;
2, 1;
6, 4, 1;
38, 22, 6, 1;
480, 232, 52, 8, 1; ...
[Row 2 of T] = [row 1 of T^2, 0] + [0, row 1 of T]:
[2, 2, 1] = [2, 1, 0] + [0, 1, 1].
Matrix cube T^3 begins:
1;
3, 1;
12, 6, 1; ...
[Row 3 of T] = [row 2 of T^3, 0] + [0, row 2 of T]:
[12, 8, 3, 1] = [12, 6, 1, 0] + [0, 2, 2, 1].
Matrix 4th power T^4 begins:
1;
4, 1;
20, 8, 1;
156, 68, 12, 1; ...
[Row 4 of T] = [row 3 of T^4, 0] + [0, row 3 of T]:
[156, 80, 20, 4, 1] = [156, 68, 12, 1, 0] + [0, 12, 8, 3, 1].

Prog

(PARI) T(n, k)=local(M=Mat(1)); if(n<k || k<0, 0, if(n==k, 1, M=matrix(n+1, n+1, r, c, if(n==k, 1, if(r>=c && r<=n, T(r-1, c-1)))); T(n-1, k-1)+(M^n)[n, k+1]))

Crossrefs

Columns: A130529, A130530, A130531.

Sequence in context: A014846 A100942 A132471 * A132986 A019112 A048660

Adjacent sequences: A130525 A130526 A130527 * A130529 A130530 A130531

Keyword

nonn,tabl

Author

Paul D. Hanna, Jun 02 2007

Status

approved