A048924 9-gonal octagonal numbers.

1, 631125, 286703855361, 130242107189808901, 59165603001256545014625, 26877395137662573622784125461, 12209701798707362366915379264832801, 5546550074879110936730454426529871893125, 2519653488703423539873583091790515645112810561, 1144613068921712475077652974503314249741447033071701

Offset

1,2

Comments

As n increases, this sequence is approximately geometric with common ratio r = lim_{n->oo} a(n)/a(n-1) = (sqrt(6) + sqrt(7))^8 = 227137 + 35048*sqrt(42). - Ant King, Jan 03 2012

References

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..100

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

Index entries for linear recurrences with constant coefficients, signature (454275,-454275,1).

Formula

a(n) = 454275*a(n-1) - 454275*a(n-2) + a(n-3). - Vincenzo Librandi, Dec 24 2011

From Ant King, Jan 03 2012: (Start)

G.f.: x*(1 + 176850*x + 261*x^2) / ((1-x)*(1 - 454274*x + x^2)).

a(n) = 454274*a(n-1) - a(n-2) + 177112.

a(n) = (1/672)*((11*sqrt(7) - 9*sqrt(6))*(sqrt(6) + sqrt(7))^(8*n-5) - (11*sqrt(7) + 9*sqrt(6))*(sqrt(6) - sqrt(7))^(8*n-5) - 262).

a(n) = floor((1/672)*(11*sqrt(7) - 9*sqrt(6))*(sqrt(6) + sqrt(7))^(8*n-5)). (End)

Mathematica

LinearRecurrence[{454275, -454275, 1}, {1, 631125, 286703855361}, 30] (* Vincenzo Librandi, Dec 24 2011 *)

Prog

(Magma) I:=[1, 631125, 286703855361]; [n le 3 select I[n] else 454275*Self(n-1)-454275*Self(n-2)+Self(n-3): n in [1..10]]; // Vincenzo Librandi, Dec 24 2011

Crossrefs

Cf. A048922, A048923.

Sequence in context: A172701 A119398 A252894 * A183678 A267362 A392344

Adjacent sequences: A048921 A048922 A048923 * A048925 A048926 A048927

Keyword

nonn,easy

Author

Eric W. Weisstein

Status

approved