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a(n) = 2^n*(3^n-3).
2

%I #15 Mar 27 2024 11:21:34

%S 0,24,192,1248,7680,46464,279552,1678848,10076160,60463104,362790912,

%T 2176770048,13060669440,78364114944,470184886272,2821109710848,

%U 16926659051520,101559955881984,609359738437632,3656158436917248,21936950634086400,131621703829684224

%N a(n) = 2^n*(3^n-3).

%C Number of orthogonal arrays OA(4,n,2,1).

%H Harry J. Smith, <a href="/A066406/b066406.txt">Table of n, a(n) for n = 1..150</a>

%H J.-Z. Zhang, Z.-S. You and Z.-L. Li, <a href="https://doi.org/10.1016/S0012-365X(01)00045-0">Enumeration of binary orthogonal arrays of strength 1</a>, Discrete Math., 239 (2000), 191-198.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-12).

%F From _Colin Barker_, Oct 20 2015: (Start)

%F a(n) = 8*a(n-1)-12*a(n-2).

%F G.f.: 24*x^2 / ((2*x-1)*(6*x-1)). (End)

%t Table[2^n(3^n-3),{n,30}] (* or *) LinearRecurrence[{8,-12},{0,24},30] (* _Harvey P. Dale_, Jul 28 2019 *)

%o (PARI) { for (n=1, 150, write("b066406.txt", n, " ", 2^n*(3^n - 3)) ) } \\ _Harry J. Smith_, Feb 13 2010

%o (PARI) concat(0, Vec(24*x^2/((2*x-1)*(6*x-1)) + O(x^30))) \\ _Colin Barker_, Oct 20 2015

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Dec 25 2001