OFFSET
0,2
COMMENTS
Self-convolution of A245926.
Limit a(n+1)/a(n) = 7 + 4*sqrt(3).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..870
FORMULA
a(n) ~ (7+4*sqrt(3))^(n+1) * (2-sqrt(3))/8 * (1+1/(3^(1/4)*sqrt(Pi*n/2))). - Vaclav Kotesovec, Aug 17 2014
D-finite with recurrence: n*a(n) +7*(-4*n+3)*a(n-1) +99*(2*n-3)*a(n-2) +7*(-4*n+9)*a(n-3) +(n-3)*a(n-4)=0. - R. J. Mathar, Jan 23 2020
EXAMPLE
G.f.: A(x) = 1 + 10*x + 127*x^2 + 1684*x^3 + 22717*x^4 + 309214*x^5 +...
MATHEMATICA
CoefficientList[Series[(1 - x + Sqrt[1 - 14*x + x^2])/(2*(1 - 14*x + x^2)), {x, 0, 50}], x] (* G. C. Greubel, Feb 14 2017 *)
PROG
(PARI) {a(n)=polcoeff( (1-x + sqrt(1-14*x+x^2 +x*O(x^n))) / (2*(1-14*x+x^2 +x*O(x^n))), n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 16 2014
STATUS
approved