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A048924 9-gonal octagonal numbers. 3
1, 631125, 286703855361, 130242107189808901, 59165603001256545014625, 26877395137662573622784125461, 12209701798707362366915379264832801, 5546550074879110936730454426529871893125 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

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

Contribution 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))^(8n-5)-(11*sqrt(7)+9*sqrt(6))*(sqrt(6)-sqrt(7))^(8n-5)-262).

a(n) = floor(1/672*(11*sqrt(7)-9*sqrt(6))*(sqrt(6)+sqrt(7))^(8n-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: A141815 A172701 A252894 * A183678 A267362 A251564

Adjacent sequences:  A048921 A048922 A048923 * A048925 A048926 A048927

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified December 3 18:46 EST 2016. Contains 278745 sequences.