A130580 Triangle, read by rows, where column k = column 0 (shifted) of matrix power T^(k+1) for k>=0, with T(0,0)=1.

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 5, 6, 4, 1, 1, 1, 9, 13, 10, 5, 1, 1, 1, 18, 30, 26, 15, 6, 1, 1, 1, 40, 76, 71, 45, 21, 7, 1, 1, 1, 98, 211, 210, 140, 71, 28, 8, 1, 1, 1, 263, 638, 673, 466, 246, 105, 36, 9, 1, 1, 1, 769, 2088, 2328, 1665, 902, 399, 148, 45, 10, 1, 1, 1

Offset

0,8

Links

Table of n, a(n) for n=0..78.

Example

Triangle T begins:
1;
1, 1;
1, 1, 1;
1, 2, 1, 1;
1, 3, 3, 1, 1;
1, 5, 6, 4, 1, 1;
1, 9, 13, 10, 5, 1, 1;
1, 18, 30, 26, 15, 6, 1, 1;
1, 40, 76, 71, 45, 21, 7, 1, 1;
1, 98, 211, 210, 140, 71, 28, 8, 1, 1;
1, 263, 638, 673, 466, 246, 105, 36, 9, 1, 1;
1, 769, 2088, 2328, 1665, 902, 399, 148, 45, 10, 1, 1; ...
Matrix square T^2 begins:
1;
2, 1;
3, 2, 1;
5, 5, 2, 1;
9, 11, 7, 2, 1;
18, 27, 19, 9, 2, 1;
40, 71, 57, 29, 11, 2, 1;
98, 202, 180, 101, 41, 13, 2, 1; ...
where column 0 of T^2 equals column 1 of T (shifted).
Matrix cube T^3 begins:
1;
3, 1;
6, 3, 1;
13, 9, 3, 1;
30, 25, 12, 3, 1;
76, 75, 40, 15, 3, 1;
211, 238, 144, 58, 18, 3, 1; ...
where column 0 of T^3 equals column 2 of T (shifted).
Matrix power T^4 begins:
1;
4, 1;
10, 4, 1;
26, 14, 4, 1;
71, 46, 18, 4, 1;
210, 159, 70, 22, 4, 1; ...
where column 0 of T^4 equals column 3 of T (shifted).

Prog

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

Crossrefs

Columns: A130581, A130582, A130583.

Sequence in context: A335570 A362644 A323718 * A220708 A110541 A331461

Adjacent sequences: A130577 A130578 A130579 * A130581 A130582 A130583

Keyword

nonn,tabl

Author

Paul D. Hanna, Jun 05 2007

Status

approved