A108296 Diagonal sums of the number triangle associated to A086617.

1, 1, 2, 3, 5, 8, 14, 24, 43, 78, 144, 269, 509, 971, 1868, 3618, 7049, 13805, 27162, 53661, 106405, 211697, 422458, 845386, 1696017, 3410522, 6873060, 13878721, 28077439, 56900936, 115501012, 234807488, 478032437, 974507543, 1989123814

Offset

0,3

Comments

The triangle associated to A086617 is given by T(n,k)=if(k<=n, sum{j=0..n-k, C(n-k,j)C(k,j)C(j)},0). A050253(n)=A108296(n+2)-A108296(n).

Links

Table of n, a(n) for n=0..34.

Formula

G.f.: (1-x^2-sqrt(1-2*x^2-4*x^3-3*x^4))/(2*x^3*(1-x^2)).

a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..n-2*k} binomial(n-2*k, j)*binomial(k, j) * A000108(j).

Conjecture: (n+3)*a(n) +(-n-2)*a(n-1) +2*(-n-1)*a(n-2) +2*(-n+3)*a(n-3) +(n+1)*a(n-4) +3*(n-2)*a(n-5)=0. - R. J. Mathar, Nov 16 2012

Crossrefs

Sequence in context: A038495 A007059 A079500 * A072100 A290075 A104882

Adjacent sequences: A108293 A108294 A108295 * A108297 A108298 A108299

Keyword

easy,nonn

Author

Paul Barry, May 31 2005

Status

approved