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A137786
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a(n) = 4^n - 3^n - 2^n.
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1
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-1, -1, 3, 29, 159, 749, 3303, 14069, 58719, 241949, 988503, 4015109, 16241679, 65506349, 263636103, 1059360149, 4251855039, 17050597949, 68331794103, 273715121189, 1096023794799, 4387584060749, 17560800790503, 70274592610229, 281192530396959, 1125052584678749
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OFFSET
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0,3
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COMMENTS
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a(n) mod 100 = 49 for n=4k+1, k>0; a(n) mod 100 = 3 for n=4k+2, k>=0. [Alex Ratushnyak, Jul 03 2012]
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LINKS
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FORMULA
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G.f.: -(1-8*x+14*x^2)/((1-2*x)*(1-3*x)*(1-4*x)). - Bruno Berselli, Jul 04 2012
a(0)=-1, a(1)=-1, a(2)=3, a(n)=9*a(n-1)-26*a(n-2)+24*a(n-3). - Harvey P. Dale, Sep 19 2012
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MAPLE
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MATHEMATICA
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LinearRecurrence[{9, -26, 24}, {-1, -1, 3}, 30] (* Harvey P. Dale, Sep 19 2012 *)
CoefficientList[Series[-(1 - 8 x + 14 x^2)/((1 - 2 x) (1 - 3 x) (1 - 4 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 12 2014 *)
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PROG
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(Python)
print([4**n - 3**n - 2**n for n in range(99)])
(Magma) I:=[-1, -1, 3]; [n le 3 select I[n] else 9*Self(n-1)-26*Self(n-2)+24*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Feb 12 2014
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CROSSREFS
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KEYWORD
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sign,easy,changed
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AUTHOR
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EXTENSIONS
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Offset set to 0, terms corrected, more terms added by Alex Ratushnyak, Jul 03 2012.
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STATUS
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approved
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