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A048924
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9-gonal octagonal numbers.
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3
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1, 631125, 286703855361, 130242107189808901, 59165603001256545014625, 26877395137662573622784125461, 12209701798707362366915379264832801, 5546550074879110936730454426529871893125
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..100
Eric Weisstein's World of Mathematics, Nonagonal Octagonal Number.
Index to sequences with linear recurrences with constant coefficients, signature (454275,-454275,1).
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FORMULA
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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)
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MATHEMATICA
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LinearRecurrence[{454275, -454275, 1}, {1, 631125, 286703855361}, 30] (* Vincenzo Librandi, Dec 24 2011 *)
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PROG
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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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CROSSREFS
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Cf. A048922, A048923.
Sequence in context: A053877 A141815 A172701 * A183678 A066590 A185476
Adjacent sequences: A048921 A048922 A048923 * A048925 A048926 A048927
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KEYWORD
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nonn,easy
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AUTHOR
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Eric W. Weisstein
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STATUS
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approved
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