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A232494 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). 0
1, 6, 32, 160, 848, 4576, 25856, 148480, 870656, 5142016, 30605312, 182640640, 1092866048, 6545268736, 39235813376, 235271618560, 1411199860736, 8465479499776, 50787717742592, 304705668382720, 1828172095029248, 10968784904912896, 65811966429495296, 394868826560266240, 2369204043294703616 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..24.

G. Wu, M. G. Parker, A complementary construction using mutually unbiased bases, arXiv preprint arXiv:1309.0157 [cs.IT], 2013 [See Th. 2].

Index entries for linear recurrences with constant coefficients, signature (8,0,-96,144)

FORMULA

G.f.: ( -1+2*x+16*x^2 ) / ( (6*x-1)*(2*x-1)*(12*x^2-1) ). - R. J. Mathar, Dec 04 2013

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

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

MAPLE

f:=proc(n)

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

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

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

MATHEMATICA

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 *)

LinearRecurrence[{8, 0, -96, 144}, {1, 6, 32, 160}, 25] (* Jean-Fran├žois Alcover, Jan 09 2019 *)

CROSSREFS

Sequence in context: A231992 A292044 A006668 * A037530 A083320 A097139

Adjacent sequences:  A232491 A232492 A232493 * A232495 A232496 A232497

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 02 2013

STATUS

approved

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Last modified August 25 05:19 EDT 2019. Contains 326318 sequences. (Running on oeis4.)