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%I #21 Jan 23 2019 02:32:27
%S 1,4,16,64,229,808,2800,9472,31705,105004,344416,1121920,3631645,
%T 11691472,37466656,119574784,380244721,1205309140,3809636848,
%U 12010028224,37773505429,118550674936,371342504848,1161099257344,3624512382793,11297181307900,35162477600704
%N a(n) = Sum_{k=0..floor(n/4)} binomial(n-3k, k)*(-3)^(3k)*4^(n-4k).
%H Vincenzo Librandi, <a href="/A248088/b248088.txt">Table of n, a(n) for n = 0..1000</a>
%H P. S. Bruckman and G. C. Greubel, <a href="https://www.fq.math.ca/Problems/MayAdvanced2014.pdf">Advanced Problem H-725</a>, Fibonacci Quarterly, 52(2):187-190, 2014.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,0,-27).
%F a(n) = 3^n*(3*n + 5)/6 - (-1)^n*3^(n+1)/2*sin((n-1)*arcsin(sqrt(2/3)))/(6*sqrt(2)).
%F G.f.: 1/(1 - 4x + 27x^4).
%F a(n) = (1+3/n)*a(n-1) + (3+6/n)*a(n-2) + (9+9/n)*a(n-3). - _Robert Israel_, Oct 27 2014
%p gser := series(1/(1-4*x+27*x^4), x = 0, 35): seq(coeff(gser, x, n), n = 0 .. 30);
%p #Alternative:
%p F:= gfun[rectoproc]({(n+4)*a(n+4)+(-7-n)*a(n+3)+(-18-3*n)*a(n+2)+(-45-9*n)*a(n+1), a(0) = 1, a(1) = 4, a(2) = 16, a(3) = 64}, a(n), remember):
%p seq(F(n),n=0..100); # _Robert Israel_, Oct 27 2014
%t CoefficientList[Series[1/(1 - 4 x + 27 x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 28 2014 *)
%o (PARI) Vec(1/(1-4*x+27*x^4)+O(x^99)) \\ _Charles R Greathouse IV_, Oct 28 2014
%K nonn,easy
%O 0,2
%A _Emeric Deutsch_, Oct 27 2014