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A046187 Indices of pentagonal numbers which are also octagonal. 3
1, 11, 1025, 12507, 1182657, 14432875, 1364784961, 16655525051, 1574960662145, 19220461475787, 1817503239330177, 22180395887532955, 2097397163226361921, 25596157633751554091, 2420394508859982326465, 29537943728953405887867, 2793133165827256378378497 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

From Ant King, Dec 16 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 16 2011: (Start)

a(n) = 1154*a(n-2) - a(n-4) - 192.

a(n) = a(n-1) + 1154*a(n-2) - 1154*a(n-3) - a(n-4) + a(n-5).

a(n) = (1/12)*((3-sqrt(2)*(-1)^n)*(1+sqrt(2))^(4*n-3) + (3 + sqrt(2)*(-1)^n)*(1-sqrt(2))^(4*n-3) + 2).

a(n) = ceiling((1/12)*(3-sqrt(2)*(-1)^n)*(1+sqrt(2))^(4*n-3)).

G.f.: x*(1-8*x-x^2)*(1+18*x+5*x^2)/((1-x)*(1-34*x+x^2)*(1+34*x+x^2)).

(End)

MATHEMATICA

LinearRecurrence[{1, 1154, -1154, -1, 1}, {1, 11, 1025, 12507, 1182657}, 15] (* Ant King, Dec 16 2011 *)

PROG

(PARI) Vec(x*(x^2+8*x-1)*(5*x^2+18*x+1)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^50)) \\ Colin Barker, Jun 23 2015

CROSSREFS

Cf. A046188, A046189.

Sequence in context: A099440 A073903 A069710 * A234634 A004811 A227323

Adjacent sequences:  A046184 A046185 A046186 * A046188 A046189 A046190

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified October 24 04:41 EDT 2021. Contains 348217 sequences. (Running on oeis4.)