A048924 9-gonal octagonal numbers.
1, 631125, 286703855361, 130242107189808901, 59165603001256545014625, 26877395137662573622784125461, 12209701798707362366915379264832801, 5546550074879110936730454426529871893125
Offset: 1
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).
Programs
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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
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Mathematica
LinearRecurrence[{454275,-454275,1},{1,631125,286703855361},30] (* Vincenzo Librandi, Dec 24 2011 *)
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)
Comments