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

Author

Gary W. Adamson, Feb 12 2009

Keywords

• nonn
• tabl

Comments

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

Examples

			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;
...
		

Links

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

Crossrefs

A156663, A122746

Programs

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

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