OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
FORMULA
Conjecture: (n+1)*a(n) +2*(1-3n)*a(n-1) +7*(n-1)*a(n-2) +2*(5-3*n)*a(n-3) +(n-3)*a(n-4)=0. - R. J. Mathar, Nov 15 2011
G.f.: (1 - 1/G(0))/(2*x), where G(k)= 1 + 4*x*(4*k+1)/( (1-x+x^2)*(4*k+2) - x*(1-x+x^2)*(4*k+2)*(4*k+3)/(x*(4*k+3) + (1-x+x^2)*(k+1)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 27 2013
G.f.: (1 - sqrt( (1 - 5*x + x^2) / (1 - x + x^2)))/(2*x). - Sergei N. Gladkovskii, Jun 27 2013
a(n) ~ sqrt(105+23*sqrt(21)) * (5+sqrt(21))^n / (sqrt(Pi) * n^(3/2) * 2^(n+7/2)). - Vaclav Kotesovec, Feb 04 2014
MATHEMATICA
CoefficientList[Series[(1 - Sqrt[(1 - 5 x + x^2)/(1 - x + x^2)])/(2 x), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 04 2014 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 07 2010
STATUS
approved