A048921 - OEIS

%I #25 Oct 11 2025 08:22:46

%S 1,26884,542041975,10928650279834,220343446399977901,

%T 4442564555387704166896,89570986345383445012986019,

%U 1805930222253056462964119954950,36411165051495138060899141518722649,734121907962314751330792028336366100956,14801365871925024964836290814418671808758991

%N 9-gonal heptagonal numbers (A000566).

%C As n increases, this sequence is approximately geometric with common ratio r = lim_{n->oo} a(n)/a(n-1) = (6+sqrt(35))^4 = 10081+1704*sqrt(35). - _Ant King_, Dec 31 2011

%D Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 44.

%H Colin Barker, <a href="/A048921/b048921.txt">Table of n, a(n) for n = 1..233</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NonagonalHeptagonalNumber.html">Nonagonal Heptagonal Number.</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (20163,-20163,1).

%F From _Ant King_, Dec 31 2011: (Start)

%F a(n) = 20163*a(n-1)-20163*a(n-2)+a(n-3).

%F a(n) = 20162*a(n-1)-a(n-2)+6768.

%F a(n) = 1/560*((39+4*sqrt(35))*(6+sqrt(35))^(4*n-3)+(39-4*sqrt(35))*(6-sqrt(35))^(4*n-3)-188).

%F a(n) = floor(1/560*(39+4*sqrt(35))*(6+sqrt(35))^(4*n-3)).

%F G.f.: x(1+6721*x+46*x^2) / ((1-x)(1-20162*x+x^2)).

%F (End)

%t LinearRecurrence[{20163, -20163, 1}, {1, 26884, 542041975}, 9]; (* _Ant King_, Dec 31 2011 *)

%o (PARI) Vec(x*(1+6721*x+46*x^2)/((1-x)*(1-20162*x+x^2)) + O(x^20)) \\ _Colin Barker_, Jun 22 2015

%Y Cf. A048919, A048920.

%K nonn,easy

%O 1,2

%A _Eric W. Weisstein_