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(5)+sqrt(6))^8 = 116161+21208*sqrt(30). - Ant King, Dec 30 2011
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..100
Eric Weisstein's World of Mathematics, Octagonal Heptagonal Number.
Index entries for linear recurrences with constant coefficients, signature (232323,-232323,1).
FORMULA
Contribution from Harvey P. Dale, Dec 09 2011: (Start)
G.f.: x*(-133*x^2-64722*x-1)/(x^3-232323*x^2+232323*x-1).
a(1)=1, a(2)=297045, a(3)=69010153345, a(n) = 232323*a(n-1)-232323*a(n-2)+a(n-3). (Start)
Contribution from Ant King, Dec 30 2011: (Start)
a(n) = 232322*a(n-1)-a(n-2)+64856.
a(n) = 1/480*((17+2*sqrt(30))*(sqrt(5)+sqrt(6))^(8n-6)+(17-2*sqrt(30))*(sqrt(5)-sqrt(6))^(8n-6)-134).
a(n) = floor(1/480*(17+2*sqrt(30))*(sqrt(5)+sqrt(6))^(8n-6)). (End)
MATHEMATICA
CoefficientList[Series[(-133*x^2-64722*x-1)/(x^3-232323*x^2+ 232323*x- 1), {x, 0, 20}], x] (* or *) LinearRecurrence[{232323, -232323, 1}, {1, 297045, 69010153345}, 21] (* Harvey P. Dale, Dec 09 2011 *)
PROG
(MAGMA) I:=[1, 297045, 69010153345]; [n le 3 select I[n] else 232323*Self(n-1)-232323*Self(n-2)+Self(n-3): n in [1..15]]; // Vincenzo Librandi, Dec 28 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved