A126125 Triangle equal to the matrix square of the triangle binomial(n,floor((n+1-(-1)^(n+k)*(k+1))/2)).

1, 2, 1, 5, 2, 1, 11, 7, 2, 1, 27, 15, 9, 2, 1, 61, 44, 19, 11, 2, 1, 149, 97, 65, 23, 13, 2, 1, 342, 267, 141, 90, 27, 15, 2, 1, 835, 599, 433, 193, 119, 31, 17, 2, 1, 1939, 1598, 956, 655, 253, 152, 35, 19, 2, 1, 4740, 3631

Offset: 0

Author

Gary W. Adamson, Dec 17 2006

Keywords

• tabl
• easy
• nonn

Comments

The triangular view of A061554 is:

1;

1, 1;

2, 1, 1;

3, 3, 1, 1;

6, 4, 4, 1, 1;

The matrix square of this (infinite) triangle is this triangle here.

Examples

			First few rows of the triangle are:
1;
2, 1;
5, 2, 1;
11, 7, 2, 1;
27, 15, 9, 2, 1;
61, 44, 19, 11, 2, 1;
..,
		

Crossrefs

Cf. A061554, A127358 (row sums).

Programs

Maple

A061554 := proc(n,k) local m ; m := floor((n+1)/2 - (-1)^(n-k)*(k+1)/2) ; binomial(n,m) ; end proc:
A126125 := proc(n,k) add(A061554(n,j)*A061554(j,k),j=k..n) ; end proc: # R. J. Mathar, Sep 17 2011