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A048907 Indices of 9-gonal numbers which are also triangular. 4
1, 10, 154, 2449, 39025, 621946, 9912106, 157971745, 2517635809, 40124201194, 639469583290, 10191389131441, 162422756519761, 2588572715184730, 41254740686435914, 657487278267789889, 10478541711598202305, 166999180107303446986, 2661508340005256949466 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
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
Eric Weisstein's World of Mathematics, Nonagonal Triangular Number.
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)
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
Sequence in context: A349490 A269608 A240196 * A061654 A298081 A240374
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)