A048920 Indices of heptagonal numbers (A000566) which are also 9-gonal.
1, 104, 14725, 2090804, 296879401, 42154784096, 5985682462189, 849924754846700, 120683329505769169, 17136182865064375256, 2433217283509635517141, 345499718075503179058724
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..200
- Eric Weisstein's World of Mathematics, Nonagonal Heptagonal Number.
- Index entries for linear recurrences with constant coefficients, signature (143,-143,1).
Programs
-
Magma
I:=[1, 104, 14725]; [n le 3 select I[n] else 143*Self(n-1)-143*Self(n-2)+Self(n-3): n in [1..30]]; // Vincenzo Librandi, Dec 21 2011
-
Mathematica
LinearRecurrence[{143,-143,1},{1,104,14725},30] (* Vincenzo Librandi, Dec 21 2011 *) -
Maxima
makelist(expand((42+(-21+5*sqrt(35))*(6+sqrt(35))^(2*n-1)-(21+5*sqrt(35))*(6-sqrt(35))^(2*n-1))/140), n, 1, 12); /* Bruno Berselli, Dec 20 2011 */
Formula
From Bruno Berselli, Dec 20 2011: (Start)
G.f.: x*(1 - 39*x - 4*x^2)/((1-x)*(1 - 142*x + x^2)).
a(n) = (42 + (-21+5r)*(6+r)^(2n-1) - (21+5r)*(6-r)^(2n-1))/140, where r=sqrt(35). (End)
From Ant King, Dec 31 2011: (Start)
a(n) = 142*a(n-1) - a(n-2) - 42.
a(n) = ceiling(1/140*(49+9*sqrt(35))*(6+sqrt(35))^(2*n-2)).
(End)
Comments