A048921 9-gonal heptagonal numbers (A000566).

1, 26884, 542041975, 10928650279834, 220343446399977901, 4442564555387704166896, 89570986345383445012986019, 1805930222253056462964119954950, 36411165051495138060899141518722649, 734121907962314751330792028336366100956, 14801365871925024964836290814418671808758991

Offset

1,2

Comments

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

References

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

Links

Colin Barker, Table of n, a(n) for n = 1..233

Eric Weisstein's World of Mathematics, Nonagonal Heptagonal Number.

Index entries for linear recurrences with constant coefficients, signature (20163,-20163,1).

Formula

From Ant King, Dec 31 2011: (Start)

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

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

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).

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

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

(End)

Mathematica

LinearRecurrence[{20163, -20163, 1}, {1, 26884, 542041975}, 9]; (* Ant King, Dec 31 2011 *)

Prog

(PARI) Vec(x*(1+6721*x+46*x^2)/((1-x)*(1-20162*x+x^2)) + O(x^20)) \\ Colin Barker, Jun 22 2015

Crossrefs

Cf. A048919, A048920.

Sequence in context: A235814 A199547 A051025 * A269115 A249496 A227348

Adjacent sequences: A048918 A048919 A048920 * A048922 A048923 A048924

Keyword

nonn,easy

Author

Eric W. Weisstein

Status

approved