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A154266
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a(n) = 27*n + 12.
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3
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12, 39, 66, 93, 120, 147, 174, 201, 228, 255, 282, 309, 336, 363, 390, 417, 444, 471, 498, 525, 552, 579, 606, 633, 660, 687, 714, 741, 768, 795, 822, 849, 876, 903, 930, 957, 984, 1011, 1038, 1065, 1092, 1119, 1146, 1173, 1200, 1227, 1254, 1281, 1308, 1335
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OFFSET
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0,1
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COMMENTS
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The identity (81*n^2 + 72*n + 17)^2 - (9*n^2 + 8*n + 2)*(27*n + 12)^2 = 1 can be written as A154295(n+1)^2 - A154262(n+1)*a(n)^2 = 1. - Vincenzo Librandi, Feb 03 2012
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (2,-1).
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FORMULA
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From R. J. Mathar, Jan 05 2011: (Start)
G.f.: 3*(4 + 5*x)/(1-x)^2.
a(n) = 3*A017209(n). (End)
a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 02 2012
E.g.f.: (27*x + 12)*exp(x). - G. C. Greubel, Sep 08 2016
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MATHEMATICA
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Range[12, 7000, 27] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)
LinearRecurrence[{2, -1}, {12, 39}, 50] (* Vincenzo Librandi, Feb 02 2012 *)
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PROG
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(PARI) a(n)=27*n+12 \\ Charles R Greathouse IV, Dec 28 2011
(MAGMA) I:=[12, 39]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]]; // Vincenzo Librandi, Feb 02 2012
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CROSSREFS
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Cf. A154262, A154295.
Sequence in context: A167712 A209872 A186779 * A236267 A119094 A226348
Adjacent sequences: A154263 A154264 A154265 * A154267 A154268 A154269
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Jan 06 2009
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EXTENSIONS
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119 replaced by 1119 - R. J. Mathar, Jan 07 2009
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STATUS
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approved
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