A046189 Octagonal pentagonal numbers.

1, 176, 1575425, 234631320, 2098015778145, 312461813932000, 2793956983975264801, 416109772078405066376, 3720751630955537773670465, 554139209013308662750166160, 4954977037463529073741814611905, 737954942591533222733596372781560

Offset

1,2

Comments

From Ant King, Dec 16 2011: (Start)

lim(n->Infinity, a(2n+1)/a(2n))=1/49*(219073+154908*sqrt(2)).

lim(n->Infinity, a(2n)/a(2n-1))=1/49*(3649+2580*sqrt(2)).

(End)

Links

Colin Barker, Table of n, a(n) for n = 1..327

Eric Weisstein's World of Mathematics, Octagonal Pentagonal Number.

Index entries for linear recurrences with constant coefficients, signature (1,1331714,-1331714,-1,1).

Formula

From Ant King, Dec 16 2011: (Start)

a(n) = 1331714*a(n-2) - a(n-4) + 249696.

a(n) = a(n-1) + 1331714*a(n-2) - 1331714*a(n-3) - a(n-4) + a(n-5).

a(n) = 1/96*((11-6*sqrt(2)*(-1)^n)*(1+sqrt(2))^(8*n-6)+(11+6*sqrt(2)*(-1)^n)*(1-sqrt(2))^(8*n-6)-18).

a(n) = floor(1/96*(11-6*sqrt(2)*(-1)^n)*(1+sqrt(2))^(8*n-6)).

G.f.: x*(1+175*x+243535*x^2+5945*x^3+40*x^4)/((1-x)*(1-1154*x+x^2)*(1+1154*x+x^2)).

(End)

Mathematica

LinearRecurrence[{1, 1331714, -1331714, -1, 1}, {1, 176, 1575425, 234631320, 2098015778145}, 11] (* Ant King, Dec 16 2011 *)

Prog

(PARI) Vec(x*(1+175*x+243535*x^2+5945*x^3+40*x^4)/((1-x)*(1-1154*x+x^2)*(1+1154*x+x^2)) + O(x^20)) \\ Colin Barker, Jun 23 2015

Crossrefs

Cf. A046187, A046188.

Sequence in context: A159426 A009722 A159442 * A278198 A164843 A268790

Adjacent sequences: A046186 A046187 A046188 * A046190 A046191 A046192

Keyword

nonn,easy

Author

Eric W. Weisstein

Status

approved