OFFSET
1,2
COMMENTS
As n increases, this sequence is approximately geometric with common ratio r = lim(n->Infinity,a(n)/a(n-1)) = (2+sqrt(5))^8 = 51841+23184*sqrt(5). -Ant King,Dec 24 2011
LINKS
Colin Barker,Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics,Heptagonal Hexagonal Number
Index entries for linear recurrences with constant coefficients,signature (103683,-103683,1).
FORMULA
FromAnt King,Dec 24 2011: (Start)
G.f.: x*(1+18088*x+55*x^2)/((1-x)*(1-103682*x+x^2)).
a(n) = 103683*a(n-1)-103683*a(n-2)+a(n-3).
a(n) = 103682*a(n-1)-a(n-2)+18144.
a(n) = 1/80*((sqrt(5)-1)*(2+sqrt(5))^(8n-5)- (sqrt(5)+1)*(2-sqrt(5))^(8n-5)-14).
a(n) = floor(1/80*(sqrt(5)-1)*(2+sqrt(5))^(8n-5)).
(End)
MATHEMATICA
LinearRecurrence[{103683, -103683, 1}, {1, 121771, 12625478965}, 8]; (*Ant King,Dec 24 2011 *)
PROG
(PARI) Vec(-x*(55*x^2+18088*x+1)/((x-1)*(x^2-103682*x+1)) + O(x^20)) \\Colin Barker,Jun 23 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved