OFFSET
1,2
COMMENTS
As n increases, this sequence is approximately geometric with common ratio r = lim_{n->oo} a(n)/a(n-1) = (2 + sqrt(5))^4 = 161 + 72*sqrt(5). - Ant King, Dec 26 2011
REFERENCES
Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 39.
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 - 102*x + 5*x^2) / ( (x-1)*(x^2 - 322*x + 1) ). - R. J. Mathar, Dec 21 2011
From Ant King, Dec 26 2011: (Start)
a(n) = 322*a(n-1) - a(n-2) - 96.
a(n) = (1/20)*((sqrt(5)+1)*(sqrt(5)+2)^(4*n-3) + (sqrt(5)-1)*(sqrt(5)-2)^(4*n-3) + 6).
a(n) = ceiling((1/20)*(sqrt(5)+1)*(sqrt(5)+2)^(4*n-3)). (End)
MATHEMATICA
LinearRecurrence[{323, -323, 1}, {1, 221, 71065}, 12]; (* Ant King, Dec 26 2011 *)
PROG
(Magma) I:=[1, 221, 71065]; [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