A048907 Indices of 9-gonal numbers which are also triangular.

1, 10, 154, 2449, 39025, 621946, 9912106, 157971745, 2517635809, 40124201194, 639469583290, 10191389131441, 162422756519761, 2588572715184730, 41254740686435914, 657487278267789889, 10478541711598202305, 166999180107303446986, 2661508340005256949466

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• easy

Comments

Entries are == 1 (mod 3). - N. J. A. Sloane, Sep 22 2007

lim(n -> Infinity, a(n)/a(n-1)) = 8 + 3*sqrt(7). - Ant King, Nov 03 2011

Links

• Colin Barker, Table of n, a(n) for n = 1..832
• Eric Weisstein's World of Mathematics, Nonagonal Triangular Number.
• Index entries for linear recurrences with constant coefficients, signature (17,-17,1).

Crossrefs

Cf. A001080, A073352, A048908, A048909.

Programs

Mathematica

LinearRecurrence[{17, -17, 1}, {1, 10, 154}, 17]; (* Ant King, Nov 03 2011 *)

PARI

Vec(-x*(x^2-7*x+1)/((x-1)*(x^2-16*x+1)) + O(x^20)) \\ Colin Barker, Jun 22 2015

Formula

G.f.: x*(1-7*x+x^2)/((1-x)*(1-16*x+x^2)).

a(n+2) = 16*a(n+1)-a(n)-5, a(n+1) = 8*a(n)-2.5+1.5*(28*a(n)^2-20*a(n)+1)^0.5. - Richard Choulet, Sep 22 2007

From Ant King, Nov 03 2011: (Start)

a(n) = 17*a(n-1) - 17*a(n-2) + a(n-3).

a(n) = ceiling(3/28*(3-sqrt(7))*(8 + 3*sqrt(7))^n).

(End)

a(n) = A097830(n-1)-7*A097830(n-2)+A097830(n-3). - R. J. Mathar, Jul 04 2024