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A048922
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Indices of 9-gonal numbers which are also octagonal.
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3
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1, 425, 286209, 192904201, 130017145025, 87631362842409, 59063408538638401, 39808649723679439625, 26830970850351403668609, 18084034544487122393202601, 12188612452013470141614884225
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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))^4 = 337+52*sqrt(42). - Ant King, Jan 03 2012
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Nonagonal Octagonal Numbers.
Index to sequences with linear recurrences with constant coefficients, signature (675,-675,1).
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FORMULA
| G.f. -x*(1-250*x+9*x^2) / ( (x-1)*(x^2-674*x+1) ). - R. J. Mathar, Dec 21 2011
Contribution from Ant King, Jan 03 2012: (Start)
a(n) = 674*a(n-1)-a(n-2)-240.
a(n) = 1/84*((sqrt(6)+3*sqrt(7))*(sqrt(6)+sqrt(7))^(4n-3)+ (sqrt(6)-3*sqrt(7))*(sqrt(6)-sqrt(7))^(4n-3)+30).
a(n) = ceiling(1/84*(sqrt(6)+3*sqrt(7))*(sqrt(6)+sqrt(7))^(4n-3)). (End)
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MATHEMATICA
| LinearRecurrence[{675, -675, 1}, {1, 425, 286209}, 30] (* Vincenzo Librandi, Dec 23 2011 *)
Join[{1}, Transpose[NestList[{Last[#], 674Last[#]-First[#]-240}&, {1, 425}, 10]][[2]]] (* From Harvey P. Dale, Feb 05 2012 *)
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PROG
| (MAGMA) I:=[1, 425, 286209]; [n le 3 select I[n] else 675*Self(n-1)-675*Self(n-2)+1*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Dec 23 2011
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CROSSREFS
| Cf. A048923, A048924.
Sequence in context: A207233 A207226 A207013 * A045094 A173374 A054984
Adjacent sequences: A048919 A048920 A048921 * A048923 A048924 A048925
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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