A048905 Indices of octagonal numbers which are also heptagonal.

1, 315, 151669, 73103983, 35235967977, 16983663460771, 8186090552123485, 3945678662460058839, 1901808929215196236753, 916667958203062126055947, 441832054044946729562729541, 212962133381706120587109582655, 102647306457928305176257256110009

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• easy

Comments

As n increases, this sequence is approximately geometric with common ratio r = lim_{n->oo} a(n)/a(n-1) = (sqrt(5)+sqrt(6))^4 = 241+44*sqrt(30). - Ant King, Dec 30 2011

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Eric Weisstein's World of Mathematics, Octagonal Heptagonal Number
• Index entries for linear recurrences with constant coefficients, signature (483,-483,1).

Crossrefs

Cf. A048904, A048906.

Programs

Mathematica

LinearRecurrence[{483,-483,1},{1,315,151669},20] (* Vincenzo Librandi, Dec 28 2011 *)

Formula

G.f.: -x*(1-168*x+7*x^2) / ( (x-1)*(x^2-482*x+1) ). - R. J. Mathar, Dec 21 2011

From Ant King, Dec 30 2011: (Start)

a(n) = 482*a(n-1)-a(n-2)-160.

a(n) = 1/120*((2*sqrt(5)+5*sqrt(6))*(sqrt(5)+sqrt(6))^(4*n-3) + (2*sqrt(5)-5*sqrt(6))*(sqrt(5)-sqrt(6))^(4*n-3)+40).

a(n) = ceiling(1/120*(2*sqrt(5)+5*sqrt(6))*(sqrt(5)+sqrt(6))^(4*n-3)). (End)