A135582 Expansion of 1/((1-x^2*c(x))(1-x-2x^2)) where c(x) is the g.f. of A000108.

1, 1, 4, 7, 18, 39, 95, 232, 606, 1663, 4839, 14807, 47330, 156611, 532308, 1846622, 6507103, 23210020, 83590477, 303425693, 1108650850, 4073443378, 15039391464, 55763147423, 207543422052, 775082175863, 2903508757053, 10907257755616

Offset

0,3

Comments

Diagonal sums of the Jacobsthal-Catalan triangle A139377.

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Formula

a(n) = Sum_{k=0..n} J(k+1)*A132364(n-k) where J(n)=A001045(n), Jacobsthal numbers.

Conjecture: (-n+1)*a(n) +6*(n-2)*a(n-1) +(-7*n+19)*a(n-2) +(-7*n+13)*a(n-3) +(13*n-31)*a(n-4) +2*(-n+4)*a(n-5) +4*(-2*n+5)*a(n-6)=0. - R. J. Mathar, Feb 23 2015

Mathematica

Jacobsthal[n_]:= (2^n - (-1)^n)/3; g[0]:= 1; g[n_] := Sum[(i/(n - i)) * Binomial[2*n - 3*i - 1, n - 2*i], {i, 0, Floor[n/2]}]; a[n_]:= Sum[Jacobsthal[k + 1]*g[n - k], {k, 0, n}]; Table[a[n], {n, 0, 25}] (* G. C. Greubel, Oct 20 2016 *)

Crossrefs

Cf. A000108, A001045, A132364.

Sequence in context: A124400 A077920 A234269 * A100828 A267488 A230601

Adjacent sequences: A135579 A135580 A135581 * A135583 A135584 A135585

Keyword

easy,nonn

Author

Paul Barry, Apr 15 2008

Status

approved