A121391 Triangle T, read by rows, where column k equals column k of T^(k+1) 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, 3, 1, 1, 1, 15, 12, 4, 1, 1, 1, 55, 58, 22, 5, 1, 1, 1, 252, 333, 146, 35, 6, 1, 1, 1, 1449, 2268, 1131, 295, 51, 7, 1, 1, 1, 10305, 18281, 10120, 2870, 521, 70, 8, 1, 1, 1, 88611, 173127, 104015, 31731, 6096, 840, 92, 9, 1, 1, 1, 901204

Offset

0,8

Links

Table of n, a(n) for n=0..67.

Example

Triangle T begins:
1;
1, 1;
1, 1, 1;
1, 2, 1, 1;
1, 5, 3, 1, 1;
1, 15, 12, 4, 1, 1;
1, 55, 58, 22, 5, 1, 1;
1, 252, 333, 146, 35, 6, 1, 1;
1, 1449, 2268, 1131, 295, 51, 7, 1, 1;
1, 10305, 18281, 10120, 2870, 521, 70, 8, 1, 1;
1, 88611, 173127, 104015, 31731, 6096, 840, 92, 9, 1, 1; ...
where column 0 of T^1 shift down 1 row equals column 0 of T.
The matrix square T^2 begins:
1;
2, 1;
3, 2, 1;
5, 5, 2, 1;
11, 15, 7, 2, 1;
34, 55, 31, 9, 2, 1;
143, 252, 165, 53, 11, 2, 1; ...
where column 1 of T^2 shift down 1 row equals column 1 of T.
The matrix cube T^3 begins:
1;
3, 1;
6, 3, 1;
13, 9, 3, 1;
36, 31, 12, 3, 1;
132, 129, 58, 15, 3, 1;
627, 663, 333, 94, 18, 3, 1; ...
where column 2 of T^3 shift down 1 row 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^j)[i-1, j]); )); A=B); return(A[n+1, k+1])}

Crossrefs

Cf. A121392 (column 1), A121393 (column 2), A121394 (column 3); variant: A121395.

Sequence in context: A090182 A256384 A111673 * A347615 A241194 A352893

Adjacent sequences: A121388 A121389 A121390 * A121392 A121393 A121394

Keyword

nonn,tabl

Author

Paul D. Hanna, Jul 27 2006

Status

approved