

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).


3



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
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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<kk<0, 0, if(n==k, 1, M=matrix(n+1, n+1, r, c, if(n==k, 1, if(r>=c&r<=n, T(r1, c1)))); T(n1, k1)+(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



