A046198 Indices of heptagonal numbers (A000566) which are also pentagonal.

1, 42, 2585, 160210, 9930417, 615525626, 38152658377, 2364849293730, 146582503552865, 9085750370983882, 563169940497447801, 34907450560470779762, 2163698764808690897425, 134114415967578364860570, 8312930091225049930457897, 515267551239985517323529026

Offset

1,2

Comments

As n increases, this sequence is approximately geometric with common ratio r = lim_{n->infinity} a(n)/a(n-1) = (4+sqrt(15))^2 = 31 + 8*sqrt(15). - Ant King, Dec 15 2011

Links

Colin Barker, Table of n, a(n) for n = 1..558

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

Index entries for linear recurrences with constant coefficients, signature (63,-63,1)

Formula

From Ant King, Dec 15 2011: (Start)

a(n) = 63*a(n-1) - 63*a(n-2) + a(n-3).

a(n) = 62*a(n-1) - a(n-2) - 18.

a(n) = (1/60)*((9-sqrt(15))*(4+sqrt(15))^(2*n-1) + (9+sqrt(15))*(4-sqrt(15))^(2*n-1)+18).

a(n) = ceiling((1/60)*(9-sqrt(15))*(4+sqrt(15))^(2*n-1)).

G.f.: x*(1-21*x+2*x^2)/((1-x)*(1-62*x+x^2)).

(End)

Mathematica

LinearRecurrence[{63, -63, 1}, {1, 42, 2585}, 14] (* Ant King, Dec 15 2011 *)

Prog

(PARI) Vec(-x*(2*x^2-21*x+1)/((x-1)*(x^2-62*x+1)) + O(x^30)) \\ Colin Barker, Jun 23 2015

Crossrefs

Cf. A046199, A048900.

Sequence in context: A187365 A294978 A180371 * A361371 A214580 A294626

Adjacent sequences: A046195 A046196 A046197 * A046199 A046200 A046201

Keyword

nonn,easy

Author

Eric W. Weisstein

Status

approved