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))^4 = 161 + 72*sqrt(5). - Ant King, Dec 24 2011
LINKS
Vincenzo Librandi, 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 (323,-323,1).
FORMULA
G.f.: x*(-1 + 76*x + 5*x^2) / ( (x-1)*(x^2 - 322*x + 1) ). - R. J. Mathar, Dec 21 2011
From Ant King, Dec 24 2011: (Start)
a(n) = 322*a(n-1) - a(n-2) - 80.
a(n) = (1/40)*sqrt(5)*((1+sqrt(5))*(sqrt(5)+2)^(4*n-3) + (1-sqrt(5))*(sqrt(5)-2)^(4*n-3) + 2*sqrt(5)).
a(n) = ceiling((1/40)*sqrt(5)*(1+sqrt(5))*(sqrt(5)+2)^(4*n-3)).
(End)
MATHEMATICA
LinearRecurrence[{323, -323, 1}, {1, 247, 79453}, 12]; (* Ant King, Dec 24 2011 *)
PROG
(Magma) I:=[1, 247, 79453]; [n le 3 select I[n] else 323*Self(n-1)-323*Self(n-2)+Self(n-3): n in [1..20]]; // Vincenzo Librandi, Dec 28 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved