OFFSET
1,2
COMMENTS
As n increases, this sequence is approximately geometric with common ratio r = lim_{n->infinity} a(n)/a(n-1) = (sqrt(6) + sqrt(7))^8 = 227137 + 35048*sqrt(42). - Ant King, Jan 03 2012
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..100
Eric Weisstein's World of Mathematics, Nonagonal Octagonal Number.
Index entries for linear recurrences with constant coefficients, signature (454275,-454275,1).
FORMULA
a(n) = 454275*a(n-1) - 454275*a(n-2) + a(n-3). - Vincenzo Librandi, Dec 24 2011
From Ant King, Jan 03 2012: (Start)
G.f.: x*(1 + 176850*x + 261*x^2) / ((1-x)*(1 - 454274*x + x^2)).
a(n) = 454274*a(n-1) - a(n-2) + 177112.
a(n) = (1/672)*((11*sqrt(7) - 9*sqrt(6))*(sqrt(6) + sqrt(7))^(8*n-5) - (11*sqrt(7) + 9*sqrt(6))*(sqrt(6) - sqrt(7))^(8*n-5) - 262).
a(n) = floor((1/672)*(11*sqrt(7) - 9*sqrt(6))*(sqrt(6) + sqrt(7))^(8*n-5)). (End)
MATHEMATICA
LinearRecurrence[{454275, -454275, 1}, {1, 631125, 286703855361}, 30] (* Vincenzo Librandi, Dec 24 2011 *)
PROG
(Magma) I:=[1, 631125, 286703855361]; [n le 3 select I[n] else 454275*Self(n-1)-454275*Self(n-2)+Self(n-3): n in [1..10]]; // Vincenzo Librandi, Dec 24 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved