A156665 Triangle read by rows, A156663 * A007318

1, 1, 1, 3, 2, 1, 3, 5, 3, 1, 7, 8, 8, 4, 1, 7, 15, 16, 12, 5, 1, 15, 22, 31, 28, 17, 6, 1, 15, 37, 53, 59, 45, 23, 7, 1, 31, 52, 90, 112, 104, 68, 30, 8, 1, 31, 83, 142, 202, 216, 172, 98, 38, 9, 1, 63, 114, 225, 344, 418, 388, 270, 136, 47, 10, 1

Offset

0,4

Comments

Row sums = A122746: (1, 2, 6, 12, 28, 56, 120,...).

Links

Robert Israel, Table of n, a(n) for n = 0..10010 (first 141 rows, flattened)

Formula

Triangle read by rows, A156663 * A007318

G.f. for triangle: 1/((1-2*x^2)*(1-x-x*y)). - Robert Israel, Aug 10 2015

Example

First few rows of the triangle =
1;
1, 1;
3, 2, 1;
3, 5, 3, 1;
7, 8, 8, 4, 1;
7, 15, 16, 12, 5, 1;
15, 22, 31, 28, 17, 6, 1;
15, 37, 53, 59, 45, 23, 7, 1;
31, 52, 90, 112, 104, 68, 30, 8, 1;
31, 83, 142, 202, 216, 172, 98, 38, 9, 1;
63, 114, 225, 344, 418, 388, 270, 136, 47, 10, 1;
...

Maple

N:= 12: # for the first N rows
A156663:= Matrix(N, N, (i, j) -> `if`((i-j)::even, 2^((i-j)/2), 0), shape=triangular[lower]):
A007318:= Matrix(N, N, (i, j) -> binomial(i-1, j-1), shape=triangular[lower]):
P:= A156663 . A007318:
seq(seq(P[i, j], j=1..i), i=1..N); # Robert Israel, Aug 10 2015

Crossrefs

A156663, A122746

Sequence in context: A318582 A318317 A129690 * A215415 A244477 A035572

Adjacent sequences: A156662 A156663 A156664 * A156666 A156667 A156668

Keyword

nonn,tabl

Author

Gary W. Adamson, Feb 12 2009

Status

approved