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

0,2

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.

Links

Table of n, a(n) for n=0..56.

Example

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;
..,

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

Crossrefs

Cf. A061554, A127358 (row sums).

Sequence in context: A104766 A361681 A105084 * A221876 A128514 A323953

Adjacent sequences: A126122 A126123 A126124 * A126126 A126127 A126128

Keyword

tabl,easy,nonn

Author

Gary W. Adamson, Dec 17 2006

Status

approved