OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
G.f.: f(z) = (1-sqrt(1-4*z*(a(0)-z*a(0)^2+z*a(1)+(k+l)*z^2/(1-z)+k*z^2/(1-z)^2)))/(2*z) (k=0, l=-1).
D-finite with recurrence: (n+1)*a(n) = 2*(3*n-1)*a(n-1) - (27 - 11*n)*a(n-2) - 4*(10*n-31)*a(n-3) + 24*(n-4)*a(n-4). - Vaclav Kotesovec, Oct 24 2012
a(n) ~ sqrt(5*sqrt(2)-3)*(4+2*sqrt(2))^n/(sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 24 2012
EXAMPLE
a(2) = 2*1*6-1 = 11. a(3) = 2*1*11+6^2-1 = 57.
MAPLE
l:=-1: : k := 0 : m:=6:d(0):=1:d(1):=m: for n from 1 to 30 do d(n+1):=sum(d(p)*d(n-p)+k, p=0..n)+l:od :
taylor((1-sqrt(1-4*z*(d(0)-z*d(0)^2+z*m+(k+l)*z^2/(1-z)+k*z^2/(1-z)^2)))/(2*z), z=0, 30); seq(d(n), n=0..30);
MATHEMATICA
Rest[CoefficientList[Series[-Sqrt[3*x+1]*Sqrt[8*x^2-8*x+1]/(2*Sqrt[1-x]), {x, 0, 20}], x]] (* Vaclav Kotesovec, Oct 24 2012 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, May 04 2010
STATUS
approved