A118040 Triangle T, read by rows, equal to the matrix square of A118032 and also equal to a diagonal bisection of A118032; i.e., diagonal n of T equals diagonal 2n of A118032: T(n,k) = A118032(2n-k,k) for n>=k>=0.

1, 2, 1, 6, 4, 1, 16, 14, 6, 1, 44, 44, 24, 8, 1, 116, 130, 84, 36, 10, 1, 294, 364, 270, 136, 50, 12, 1, 748, 990, 780, 476, 200, 66, 14, 1, 1794, 2540, 2268, 1400, 760, 276, 84, 16, 1, 4352, 6514, 5832, 4332, 2260, 1134, 364, 104, 18, 1, 10072, 15640, 15876, 11128

Offset

0,2

Comments

Rows of this triangle form even-indexed antidiagonals of A118032; thus the row sums form a bisection of the antidiagonal sums of A118032.

Links

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

Example

Triangle T begins:
1;
2, 1;
6, 4, 1;
16, 14, 6, 1;
44, 44, 24, 8, 1;
116, 130, 84, 36, 10, 1;
294, 364, 270, 136, 50, 12, 1;
748, 990, 780, 476, 200, 66, 14, 1;
1794, 2540, 2268, 1400, 760, 276, 84, 16, 1;
4352, 6514, 5832, 4332, 2260, 1134, 364, 104, 18, 1;
10072, 15640, 15876, 11128, 7410, 3396, 1610, 464, 126, 20, 1; ...
and is the matrix square of triangle A118032, which starts:
1;
1, 1;
2, 2, 1;
3, 4, 3, 1;
6, 8, 6, 4, 1;
9, 14, 15, 8, 5, 1;
16, 28, 24, 24, 10, 6, 1;
26, 44, 57, 36, 35, 12, 7, 1;
44, 86, 84, 96, 50, 48, 14, 8, 1; ...
where even-indexed diagonals of A118032 form the diagonals of T.

Crossrefs

Columns: A118041, A118042, A118043; A118044 (row sums); related triangles: A118032, A118045.

Sequence in context: A250485 A269505 A269479 * A073387 A259099 A125693

Adjacent sequences: A118037 A118038 A118039 * A118041 A118042 A118043

Keyword

nonn,tabl

Author

Paul D. Hanna, Apr 10 2006

Status

approved