A118045 Triangle T, read by rows, equal to a diagonal bisection of A118032 such that diagonal n of T equals diagonal 2n+1 of A118032: T(n,k) = A118032(2n+1-k,k); also equals the matrix product of A118032 and SHIFT_UP(A118032).

1, 3, 2, 9, 8, 3, 26, 28, 15, 4, 73, 86, 57, 24, 5, 191, 250, 192, 96, 35, 6, 500, 696, 567, 356, 145, 48, 7, 1234, 1824, 1683, 1060, 590, 204, 63, 8, 3051, 4754, 4392, 3344, 1765, 906, 273, 80, 9, 7201, 11562, 12084, 8672, 5895, 2718, 1316, 352, 99, 10, 16995

Offset

0,2

Links

Table of n, a(n) for n=0..55.

Example

Triangle begins:
1;
3, 2;
9, 8, 3;
26, 28, 15, 4;
73, 86, 57, 24, 5;
191, 250, 192, 96, 35, 6;
500, 696, 567, 356, 145, 48, 7;
1234, 1824, 1683, 1060, 590, 204, 63, 8;
3051, 4754, 4392, 3344, 1765, 906, 273, 80, 9;
7201, 11562, 12084, 8672, 5895, 2718, 1316, 352, 99, 10; ...
which is formed from the odd-indexed diagonals 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; ...
Let U = SHIFT_UP(A118032), shifting columns of A118032 up 1 row
and dropping the main diagonal, so that U =
1;
2, 2;
3, 4, 3;
6, 8, 6, 4;
9, 14, 15, 8, 5;
16, 28, 24, 24, 10, 6; ...
Then the matrix product A118032*U equals this triangle.

Crossrefs

. columns: A118046, A118047, A118048; A118049 (row sums); related triangles: A118032, A118040.

Sequence in context: A124003 A159588 A321572 * A276023 A268822 A201926

Adjacent sequences: A118042 A118043 A118044 * A118046 A118047 A118048

Keyword

nonn,tabl

Author

Paul D. Hanna, Apr 10 2006

Status

approved