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A084858
Binomial transform of A001651.
11
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
OFFSET
0,2
COMMENTS
a(n+1)/3 = A001792(n).
FORMULA
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
MATHEMATICA
CoefficientList[Series[(x^2-x+1)/(1-2x)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 24 2012 *)
PROG
(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
CROSSREFS
Sequence in context: A034330 A264685 A320731 * A228820 A335470 A003262
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jun 11 2003
STATUS
approved