OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1400
FORMULA
G.f.: (1-x^2- sqrt(1-4*x-6*x^2+x^4))/(2*x).
G.f.: (1+x)/(1-x^2-x/(1-x-x/(1-x^2-x/(1-x-x/(1-...))))) (continued fraction).
a(n) = Sum{k=0..n, A000108(k)*Sum{i=0..floor(n/2), C(n-2i,n-2i-k)*C(k+i-1,i)}}.
Conjecture: (n+1)*a(n) +(n+2)*a(n-1) +(42-26*n)*a(n-2) +30*(3-n)*a(n-3) +(n-5)*a(n-4) +5*(n-6)*a(n-5)=0. - R. J. Mathar, Nov 15 2011
G.f. A(x) satisfies: A(x) = 1 + x * (1 + x*A(x) + A(x)^2). - Ilya Gutkovskiy, Jul 01 2020
MATHEMATICA
CoefficientList[Series[(1-x^2 - Sqrt[1-4*x-6*x^2+x^4])/(2*x), {x, 0, 50}], x] (* G. C. Greubel, Aug 14 2018 *)
PROG
(PARI) x='x+O('x^30); Vec((1-x^2- sqrt(1-4*x-6*x^2+x^4))/(2*x)) \\ G. C. Greubel, Aug 14 2018
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x^2- Sqrt(1-4*x-6*x^2+x^4))/(2*x))); // G. C. Greubel, Aug 14 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Mar 28 2011
STATUS
approved