%I #24 Jan 09 2019 09:11:47

%S 1,6,32,160,848,4576,25856,148480,870656,5142016,30605312,182640640,

%T 1092866048,6545268736,39235813376,235271618560,1411199860736,

%U 8465479499776,50787717742592,304705668382720,1828172095029248,10968784904912896,65811966429495296,394868826560266240,2369204043294703616

%N If n mod 2 = 0 then 2^(n-1)*(3^n+3*3^(n/2)-2) otherwise 2^(n-1)*(3^n+5*3^((n-1)/2)-2).

%H G. Wu, M. G. Parker, <a href="http://arxiv.org/abs/1309.0157">A complementary construction using mutually unbiased bases</a>, arXiv preprint arXiv:1309.0157 [cs.IT], 2013 [See Th. 2].

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,0,-96,144)

%F G.f.: ( -1+2*x+16*x^2 ) / ( (6*x-1)*(2*x-1)*(12*x^2-1) ). - _R. J. Mathar_, Dec 04 2013

%F a(n) = 2^(n-2) * (2 * 3^n - 4 + 3^((n-1)/2)(5 + 3*sqrt(3) + (-1)^n * (3*sqrt(3) - 5))). - _Benedict W. J. Irwin_, Sep 27 2016

%F E.g.f.: (1/12)*exp(-2*sqrt(3)*x)*(9 - 5*sqrt(3) + (9 + 5*sqrt(3))*exp(4*sqrt(3)*x) - 12*exp(2*(1 + sqrt(3))*x) + 6*exp(2*(3 + sqrt(3))*x)). - _Stefano Spezia_, Jan 09 2019

%p f:=proc(n)

%p if (n mod 2) = 0 then 2^(n-1)*(3^n+3*3^(n/2)-2) else

%p 2^(n-1)*(3^n+5*3^((n-1)/2)-2) fi; end;

%p [seq(f(n),n=0..40)];

%t Table[2^(n - 2) * (-4 + 2 3^n + 3^(n/2 - 1/2)(5 - 5(-1)^n + 3Sqrt[3] + 3(-1)^n Sqrt[3])), {n, 0, 20}] (* _Benedict W. J. Irwin_, Sep 27 2016 *)

%t LinearRecurrence[{8, 0, -96, 144}, {1, 6, 32, 160}, 25] (* _Jean-François Alcover_, Jan 09 2019 *)

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Dec 02 2013