OFFSET
1,2
COMMENTS
From Ant King, Dec 20 2011: (Start)
lim(n->Infinity, a(2n+1)/a(2n))=1/2*(527+115*sqrt(21))
lim(n->Infinity, a(2n)/a(2n-1))=1/2*(23+5*sqrt(21))
(End)
LINKS
Colin Barker, Table of n, a(n) for n = 1..490
Eric Weisstein's World of Mathematics, Nonagonal Pentagonal Number.
Index entries for linear recurrences with constant coefficients, signature (1,12098,-12098,-1,1).
FORMULA
From Ant King, Dec 20 2011: (Start)
a(n) = 12098*a(n-2)-a(n-4)-2016.
a(n) = a(n-1)+12098*a(n-2)-12098*a(n-3)-a(n-4)+a(n-5).
a(n) = 1/84*((2+sqrt(21))*(7-sqrt(21)*(-1)^n)*(2*sqrt(7)+3*sqrt(3))^(2n-2)+ (2-sqrt(21))*(7+sqrt(21)*(-1)^n)*(2*sqrt(7)-3*sqrt(3))^(2n-2)+14).
a(n) = ceiling(1/84*(2+sqrt(21))*(7-sqrt(21)*(-1)^n)*(2*sqrt(7)+3*sqrt(3))^(2n-2)).
G.f.: x*(1+20*x-1138*x^2-860*x^3-39*x^4) / ((1-x)*(1-110*x+x^2)*(1+110*x+x^2))
(End)
MATHEMATICA
LinearRecurrence[{1, 12098, -12098, -1, 1}, {1, 21, 10981, 252081, 132846121}, 13] (* Ant King, Dec 20 2011 *)
PROG
(PARI) Vec(x*(39*x^4+860*x^3+1138*x^2-20*x-1)/((x-1)*(x^2-110*x+1)*(x^2+110*x+1)) + O(x^20)) \\ Colin Barker, Jun 22 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved