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
Programs
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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 *)
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
Comments