A121395 Triangle T, read by rows, where column k equals column k of T^(2^k) shift down 1 row, with T(n,n)=T(n+1,n)=1 for n>=0.

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 4, 1, 1, 1, 16, 22, 8, 1, 1, 1, 75, 164, 92, 16, 1, 1, 1, 594, 1837, 1464, 376, 32, 1, 1, 1, 8420, 34176, 35190, 12336, 1520, 64, 1, 1, 1, 212790, 1106012, 1393400, 612316, 101216, 6112, 128, 1, 1, 1, 9542280, 63053480, 95005100

Offset

0,8

Links

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

Example

Triangle begins:
1;
1, 1;
1, 1, 1;
1, 2, 1, 1;
1, 5, 4, 1, 1;
1, 16, 22, 8, 1, 1;
1, 75, 164, 92, 16, 1, 1;
1, 594, 1837, 1464, 376, 32, 1, 1;
1, 8420, 34176, 35190, 12336, 1520, 64, 1, 1;
1, 212790, 1106012, 1393400, 612316, 101216, 6112, 128, 1, 1; ...
where column 0 of T^(2^0) equals column 0 of T.
The matrix square T^2 begins:
1;
2, 1;
3, 2, 1;
5, 5, 2, 1;
12, 16, 9, 2, 1;
49, 75, 56, 17, 2, 1;
350, 594, 506, 208, 33, 2, 1; ...
where column 1 of T^(2^1) equals column 1 of T.
The matrix 4th power T^4 begins:
1;
4, 1;
10, 4, 1;
26, 14, 4, 1;
93, 60, 22, 4, 1;
525, 379, 164, 38, 4, 1;
4940, 3918, 1837, 516, 70, 4, 1; ...
where column 2 of T^(2^2) equals column 2 of T.

Prog

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

Crossrefs

Cf. A121396 (column 1), A121397 (column 2).

Sequence in context: A181196 A227578 A181783 * A275377 A384437 A219585

Adjacent sequences: A121392 A121393 A121394 * A121396 A121397 A121398

Keyword

nonn,tabl

Author

Paul D. Hanna, Jul 27 2006

Status

approved