A248089 a(n) = Sum_{k=0..floor(n/4)} binomial(n-k, 3k)*(-3)^(3k)*4^(n-4k).

1, 4, 16, 64, 229, 592, -224, -18176, -175655, -1265732, -7914560, -44970752, -236014307, -1145932664, -5086940240, -19929220352, -61944816911, -81359219468, 858917862064, 10785877546432, 84667993188757, 555461238134080, 3268576565244544, 17688312222825472, 88631554966652233, 408731119650234796

Offset

0,2

Links

Table of n, a(n) for n=0..25.

P. S. Bruckman and G. C. Greubel, Advanced Problem H-725, Fibonacci Quarterly, 52(2):187-190, 2014.

Index entries for linear recurrences with constant coefficients, signature (12,-48,64,-27).

Formula

a(n) = (9n + 7 + 3^(3n/2)*(11*sqrt(2)*cos(n*arcsin(sqrt(2/27))) + sin(n*arcsin(sqrt(2/27))))/sqrt(2))/18.

G.f.: (1-4x)^2/((1-4x)^3+27x^4) = (1-4*x)^2/((x-1)^2*(1 - 10*x + 27*x^2)).

Maple

Gser:=series((1-4*x)^2/((1-4*x)^3+27*x^4), x = 0, 35): seq(coeff(Gser, x, n), n = 0 .. 30);

Mathematica

LinearRecurrence[{12, -48, 64, -27}, {1, 4, 16, 64}, 30] (* Harvey P. Dale, Nov 21 2015 *)

Crossrefs

Sequence in context: A189336 A262334 A065738 * A248088 A294037 A228735

Adjacent sequences: A248086 A248087 A248088 * A248090 A248091 A248092

Keyword

sign,easy

Author

Emeric Deutsch, Oct 27 2014

Status

approved