A186341 a(n)=sum{k=0..floor(n/2), binomial(n-k,k)*A186338(k)}.

1, 1, 3, 5, 15, 33, 95, 237, 667, 1765, 4943, 13505, 37967, 105837, 299675, 847253, 2417903, 6909409, 19866303, 57253165, 165728475, 480938693, 1400391247, 4087481409, 11963060527, 35089773869, 103157489499, 303856951925, 896755068783, 2651120922081, 7850714948511

Offset

0,3

Comments

Hankel transform is A134751.

Links

Table of n, a(n) for n=0..30.

Formula

G.f.: 1/(1-x-2x^2/(1-2x^2/(1-x-x^2/(1-2x^2/(1-x-2x^2/(1-x^2/(1-x-2x^2/(1-... (continued fraction).

G.f.: (1-x-3x^2-sqrt((1-3x-7x^2+19x^3+15x^4-25x^5-16x^6)/(1-x)))/(2x^2(1-x-2x^2)).

Conjecture: (n+2)*a(n) +5*(-n-1)*a(n-1) +2*(-n+3)*a(n-2) +(38*n-59)*a(n-3) +(-22*n+41)*a(n-4) +4*(-22*n+81)*a(n-5) +3*(19*n-79)*a(n-6) +3*(29*n-164)*a(n-7) +2*(-17*n+98)*a(n-8) +16*(-2*n+15)*a(n-9)=0. - R. J. Mathar, Oct 08 2016

Mathematica

CoefficientList[Series[(1-x-3x^2-Sqrt[(1-3x-7x^2+19x^3+15x^4-25x^5-16x^6)/(1-x)])/(2x^2(1-x-2x^2)), {x, 0, 40}], x]  (* Harvey P. Dale, Mar 04 2011 *)

Crossrefs

Sequence in context: A120748 A182143 A193649 * A262326 A148499 A148500

Adjacent sequences: A186338 A186339 A186340 * A186342 A186343 A186344

Keyword

nonn,easy

Author

Paul Barry, Feb 18 2011

Status

approved