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A084858
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Binomial transform of A001651.
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11
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1, 3, 9, 24, 60, 144, 336, 768, 1728, 3840, 8448, 18432, 39936, 86016, 184320, 393216, 835584, 1769472, 3735552, 7864320, 16515072, 34603008, 72351744, 150994944, 314572800, 654311424, 1358954496, 2818572288, 5838471168, 12079595520
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OFFSET
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0,2
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COMMENTS
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a(n+1)/3 = A001792(n).
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-4).
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FORMULA
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G.f.: (x^2 - x + 1)/(1-2*x)^2.
a(n) = 3*(0^n/3 + 2^n + n*2^n)/4.
For n > 1: a(n) = 2*a(n-1) + 3*2^(n-2). - Philippe Deléham, Nov 10 2011
a(n) = 4*a(n-1) - 4*a(n-2). - Vincenzo Librandi, Jun 24 2012
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MATHEMATICA
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CoefficientList[Series[(x^2-x+1)/(1-2x)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 24 2012 *)
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PROG
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(PARI) a(n)=3*(0^n/3+2^n+n<<n)/4 \\ Charles R Greathouse IV, Nov 11 2011
(MAGMA) I:=[1, 3, 9]; [n le 3 select I[n] else 4*Self(n-1)-4*Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jun 24 2012
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CROSSREFS
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Sequence in context: A034330 A264685 A320731 * A228820 A335470 A003262
Adjacent sequences: A084855 A084856 A084857 * A084859 A084860 A084861
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Jun 11 2003
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STATUS
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approved
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