A048908 Indices of triangular numbers which are also 9-gonal.

1, 25, 406, 6478, 103249, 1645513, 26224966, 417953950, 6661038241, 106158657913, 1691877488374, 26963881156078, 429730221008881, 6848719654986025, 109149784258767526, 1739547828485294398, 27723615471505942849, 441838299715609791193, 7041689179978250716246

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• easy

Comments

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. A048907, A048909.

Programs

Mathematica

LinearRecurrence[{17, -17, 1}, {1, 25, 406}, 16]; (* Ant King, Nov 03 2011 *)

PARI

Vec(x*(2*x^2-8*x-1)/((x-1)*(x^2-16*x+1)) + O(x^50)) \\ Colin Barker, Jun 22 2015

Formula

a(n+2) = 16*a(n+1)-a(n)+7, a(n+1) = 8*a(n)+3.5+1.5*(28*a(n)^2+28*a(n)+25)^0.5 - Richard Choulet, Sep 22 2007

G.f.: f(z) = a(1)*z+a(2)*z^2+... = (z+8z^2-2*z^3)/((1-z)*(1-16*z+z^2)) - Richard Choulet, Oct 09 2007

From Ant King, Nov 03 2011: (Start)

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

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

(End)