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, 42417134259976807744465

Offset

1,2

Comments

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

References

Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 42.

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).

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).

Limit_{n ->oo} a(n)/a(n-1) = 8 + 3*sqrt(7). (End)

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001080, A073352, A048908, A048909.

Sequence in context: A349490 A269608 A240196 * A061654 A298081 A385475

Adjacent sequences: A048904 A048905 A048906 * A048908 A048909 A048910

Keyword

nonn,easy

Author

Eric W. Weisstein

Status

approved