OFFSET
1,2
REFERENCES
Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 40.
LINKS
Colin Barker, Table of n, a(n) for n = 1..654
Eric Weisstein's World of Mathematics, Octagonal Pentagonal Number.
Index entries for linear recurrences with constant coefficients, signature (1,1154,-1154,-1,1).
FORMULA
From Ant King, Dec 17 2011: (Start)
a(n) = 1154*a(n-2) - a(n-4) - 384.
a(n) = a(n-1) + 1154*a(n-2) - 1154*a(n-3) - a(n-4) + a(n-5).
a(n) = (1/24)*sqrt(2)*((3-sqrt(2)*(-1)^n)*(1+sqrt(2))^(4*n-3) - (3+sqrt(2)*(-1)^n)*(1-sqrt(2))^(4*n-3) + 4*sqrt(2)).
a(n) = ceiling((1/24)*sqrt(2)*((3-sqrt(2)*(-1)^n)*(1+sqrt(2))^(4*n-3))).
G.f.: x*(1 + 7*x - 437*x^2 + 41*x^3 + 4*x^4)/((1-x)*(1 - 34*x + x^2)*(1 + 34*x + x^2)).
Limit_{n->oo} a(2n+1)/a(2n) = (1/7)*(331 + 234*sqrt(2)).
Limit_{n->oo} a(2n)/a(2n-1) = (1/7)*(43 + 30*sqrt(2)). (End)
MATHEMATICA
LinearRecurrence[{1, 1154, -1154, -1, 1}, {1, 8, 725, 8844, 836265}, 15] (* Ant King, Dec 17 2011 *)
PROG
(PARI) Vec(-x*(4*x^4+41*x^3-437*x^2+7*x+1)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^50)) \\ Colin Barker, Jun 23 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved