A124788 Triangle read by rows: expansion of (1+x*y)/(1-x^2*y^2-x^3*y^2).

1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0, 0, 0, 3, 3, 1, 0, 0, 0, 0, 0, 0, 1, 3, 4, 1, 0, 0, 0, 0, 0, 0, 0, 1, 6, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 10, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 10, 10, 6

Offset

0,20

Comments

Row sums give A000931(n+5). Diagonal sums are A124789.

Links

Table of n, a(n) for n=0..103.

Formula

Number triangle T(n,k) = binomial(floor(k/2),n-k).

Column k has g.f. x^k*(1+x)^floor(k/2). - Paul Barry, Feb 01 2007

Example

Triangle begins
1,
0, 1,
0, 0, 1,
0, 0, 1, 1,
0, 0, 0, 1, 1,
0, 0, 0, 0, 2, 1,
0, 0, 0, 0, 1, 2, 1,
0, 0, 0, 0, 0, 1, 3, 1,
0, 0, 0, 0, 0, 0, 3, 3, 1,
0, 0, 0, 0, 0, 0, 1, 3, 4, 1,
0, 0, 0, 0, 0, 0, 0, 1, 6, 4, 1

Maple

A124788 := proc(n, k) binomial(floor(k/2), n-k) ; end: for n from 0 to 20 do for k from 0 to n do printf("%d, ", A124788(n, k)) ; od ; od ; # R. J. Mathar, Feb 10 2007

Crossrefs

Cf. A124745.

Sequence in context: A227839 A291748 A124744 * A284504 A281245 A284499

Adjacent sequences: A124785 A124786 A124787 * A124789 A124790 A124791

Keyword

easy,nonn,tabl

Author

Paul Barry, Nov 07 2006

Extensions

More terms from R. J. Mathar, Feb 10 2007

Status

approved