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A046188 Indices of octagonal numbers which are also pentagonal. 3
1, 8, 725, 8844, 836265, 10205584, 965048701, 11777234708, 1113665364305, 13590918647064, 1285168865358885, 15683908341476764, 1483083756958788601, 18099216635145538208, 1711477370361576686285, 20886480313049609614884, 1975043402313502537183905 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

From Ant King, Dec 17 2011: (Start)

lim_{n->infinity} a(2n+1)/a(2n) = (1/7)*(331 + 234*sqrt(2)).

lim_{n->infinity} a(2n)/a(2n-1) = (1/7)*(43 + 30*sqrt(2)).

(End)

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)).

(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

Cf. A046187, A046189.

Sequence in context: A277860 A221198 A071308 * A014387 A220641 A017007

Adjacent sequences:  A046185 A046186 A046187 * A046189 A046190 A046191

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified July 22 05:47 EDT 2019. Contains 325213 sequences. (Running on oeis4.)