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A087452
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G.f.: (2-x)/((1+3x)(1-4x)); e.g.f.: exp(4x)+exp(-3x); a(n)=4^n+(-3)^n.
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1
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2, 1, 25, 37, 337, 781, 4825, 14197, 72097, 242461, 1107625, 4017157, 17308657, 65514541, 273218425, 1059392917, 4338014017, 17050729021, 69106897225, 273715645477, 1102998412177, 4387586157901, 17623567104025, 70274600998837, 281757406247137
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OFFSET
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0,1
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COMMENTS
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Generalized Lucas-Jacobsthal numbers.
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LINKS
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Table of n, a(n) for n=0..24.
Index to sequences with linear recurrences with constant coefficients, signature (1,12).
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FORMULA
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The sequence 1, 25, 35, ... is 4*4^n-3*(-3)^n.
a(0)=2, a(1)=1, a(n)=a(n-1)+12*a(n-2) for n>1. [From Philippe DELEHAM, Sep 19 2009]
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MATHEMATICA
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CoefficientList[Series[(2 - z)/((1 + 3 z) (1 - 4 z)), {z, 0, 200}], z] (* From Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *)
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PROG
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(PARI) polsym(x^2-x-12, 50) \\ Charles R Greathouse IV, Jun 11 2011
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CROSSREFS
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Cf. A014551, A087451.
Sequence in context: A013313 A013317 A010256 * A098878 A138955 A089963
Adjacent sequences: A087449 A087450 A087451 * A087453 A087454 A087455
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KEYWORD
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easy,nonn,changed
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AUTHOR
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Paul Barry, Sep 06 2003
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STATUS
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approved
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