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A048924
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9-gonal octagonal numbers.
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4
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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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FORMULA
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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)
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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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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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