OFFSET
0,3
COMMENTS
Limiting ratio is 1.4408839873261408 ... .
REFERENCES
Henry McKean and Victor Moll, Elliptic Curves - Function Theory, Geometry, Arithmetic. Cambridge University Press, New York, 1999, page 173 (ISBN-13: 978-0521658171).
LINKS
Georg Fischer, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,1,0,0,0,0,0,0,0,0,0,-1,0,1,1,-1,-1).
FORMULA
G.f.: 1 / ( (x-1)*(1+x)*(x^18+x^17+x^13+x^11+x^9+x^7+x^5+x-1) ).
MATHEMATICA
f[x_] = 1 - x^2 + x^3 + x^4 - x^5;
p[x_] = ExpandAll[x^5*f[-1/x] - x^(5 + 10)*f[x]];
f[x_] = ExpandAll[x^20*p[1/x]]
a = Table[SeriesCoefficient[
Series[1/f[x], {x, 0, 100}], n], {n, 0, 100}]
(* or *) LinearRecurrence[{1, 1, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 1, -1, -1}, {1, 1, 2, 2, 3, 4, 6, 9, 13, 19, 27, 39, 56, 81, 117, 168, 242, 348, 503, 725}, 1001] (* Georg Fischer, signature from Colin Barker, Feb 28 2019 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Nov 29 2010
STATUS
approved