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Number of additive Z_2 Z_8 codes of a certain type (see Siap-Aydogdu for precise definition).
9

%I #22 Sep 01 2018 17:37:21

%S 36,84,180,372,756,1524,3060,6132,12276,24564,49140,98292,196596,

%T 393204,786420,1572852,3145716,6291444,12582900,25165812,50331636,

%U 100663284,201326580,402653172,805306356,1610612724,3221225460,6442450932,12884901876,25769803764

%N Number of additive Z_2 Z_8 codes of a certain type (see Siap-Aydogdu for precise definition).

%C N2×8(r+1, 2; r, 1, 1, 0) r>=1. (Siap-Aydogdu Table 1)

%H Lars Blomberg, <a href="/A226264/b226264.txt">Table of n, a(n) for n = 1..100</a>

%H I. Siap and I. Aydogdu, <a href="http://arxiv.org/abs/1303.6985">Counting The Generator Matrices of Z_2 Z_8 Codes</a>, arXiv preprint arXiv:1303.6985 [math.CO], 2013.

%F Conjectures from _Colin Barker_, Jun 14 2017: (Start)

%F G.f.: 12*x*(3 - 2*x) / ((1 - x)*(1 - 2*x)).

%F a(n) = 12*(2^(1+n) - 1) for n>0.

%F a(n) = 3*a(n-1) - 2*a(n-2) for n>2.

%F (End)

%t QP = QPochhammer;

%t a[n_] := 2(6(2^(n+3))^n QP[2^(-n-1), 2, n])/((2^(n+2))^n QP[2^-n, 2, n]);

%t Array[a, 30] (* _Jean-François Alcover_, Sep 01 2018 *)

%Y Cf. A226262, A226263, A226265, A226266, A226267, A226268.

%K nonn

%O 1,1

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

%E Terms a(6) and beyond from _Lars Blomberg_, Jun 14 2017