A108361 Diagonal sums of number triangle A108359.

1, 1, 2, 4, 7, 13, 25, 47, 90, 172, 329, 629, 1202, 2294, 4374, 8330, 15847, 30115, 57172, 108434, 205473, 389019, 735927, 1391121, 2627720, 4960134, 9356707, 17639323, 33234036, 62580444, 117776828, 221542596, 416524573, 782743029

Offset

0,3

Links

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (3,0,-4,-2,2,4,0,-1,-1).

Formula

a(n) = sum{k=0..floor(n/2)} ( sum{j=0..n-2k} C(k, j) * C(n-k-j, k) * floor((j+2)/2) ).

Empirical g.f.: (x^2+x-1)^2 / ((x-1)^2*(x+1)*(x^3+x^2+x-1)^2). - Colin Barker, Sep 26 2014

Maple

A108361:=n->add(add(binomial(k, j)*binomial(n-k-j, k)*floor((j+2)/2), j=0..n-2*k), k=0..floor(n/2)): seq(A108361(n), n=0..50); # Wesley Ivan Hurt, Sep 26 2014

Mathematica

Table[Sum[Sum[Binomial[k, j] Binomial[n - k - j, k] Floor[(j + 2)/2], {j, 0, n - 2 k}], {k, 0, Floor[n/2]}], {n, 0, 30}] (* Wesley Ivan Hurt, Sep 26 2014 *)

Crossrefs

Cf. A108359.

Sequence in context: A367400 A018082 A018083 * A082423 A176485 A119266

Adjacent sequences: A108358 A108359 A108360 * A108362 A108363 A108364

Keyword

easy,nonn

Author

Paul Barry, May 31 2005

Status

approved