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A083086
a(n) = (2^(n+1) + (-4)^n)/3.
5
1, 0, 8, -16, 96, -320, 1408, -5376, 22016, -87040, 350208, -1396736, 5595136, -22364160, 89489408, -357892096, 1431699456, -5726535680, 22906667008, -91625619456, 366504574976, -1466014105600, 5864064811008, -23456242466816, 93825003421696, -375299946577920
OFFSET
0,3
COMMENTS
Binomial transform of A083085.
FORMULA
a(n) = (2*2^n + (-4)^n)/3.
G.f.: (1+2*x)/((1+4*x)*(1-2*x)).
E.g.f.: (2*exp(2*x) + exp(-4*x))/3.
a(n) = (-1)^n*A000079(n)*A078008(n). - Paul Barry, Feb 12 2004
a(n) = -2*a(n-1) + 8*a(n-2). - Vincenzo Librandi, Nov 12 2011
MATHEMATICA
LinearRecurrence[{-2, 8}, {1, 0}, 41] (* G. C. Greubel, Feb 19 2023 *)
PROG
(Magma) [(2*2^n+(-4)^n)/3: n in [0..30]]; // Vincenzo Librandi, Nov 12 2011
(PARI) a(n)=(2*2^n+(-4)^n)/3 \\ Charles R Greathouse IV, Oct 07 2015
(SageMath) [(2^(n+1)+(-4)^n)/3 for n in range(41)] # G. C. Greubel, Feb 19 2023
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Paul Barry, Apr 23 2003
STATUS
approved