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A225832 Number of binary pattern classes in the (8,n)-rectangular grid: two patterns are in the same class if one of them can be obtained by a reflection or 180-degree rotation of the other.

%I A225832 #33 Sep 08 2022 08:46:05
%S A225832 1,136,16576,4212736,1073790976,274882625536,70368756760576,
%T A225832 18014399717441536,4611686021648613376,1180591621026648948736,
%U A225832 302231454904481927397376,77371252455415432018395136,19807040628566295504618520576
%N A225832 Number of binary pattern classes in the (8,n)-rectangular grid: two patterns are in the same class if one of them can be obtained by a reflection or 180-degree rotation of the other.
%H A225832 Vincenzo Librandi, <a href="/A225832/b225832.txt">Table of n, a(n) for n = 0..400</a>
%H A225832 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (256,256,-65536).
%F A225832 a(n) = 2^8*a(n-1) + 2^8*a(n-2) - (2^8)^2*a(n-3), with n>2, a(0)=1, a(1)=136, a(2)=16576.
%F A225832 a(n) = 2^(4n-3)*(2^(4n+1)-(2^4-1)*(-1)^n+2^4+5).
%F A225832 G.f.: (1-120*x-18496*x^2)/((1-16*x)*(1+16*x)*(1-256*x)).
%t A225832 CoefficientList[Series[(1 - 120 x - 18496 x^2) / ((1 - 16 x) (1 + 16 x) (1 - 256 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Sep 04 2013 *)
%o A225832 (Magma) I:=[1,136,16576]; [n le 3 select I[n] else 256*Self(n-1)+256*Self(n-2)-65536*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Sep 04 2013
%Y A225832 A005418 is the number of binary pattern classes in the (1,n)-rectangular grid.
%Y A225832 A225826 to A225834  are the numbers of binary pattern classes in the (m,n)-rectangular grid, 1 < m < 11 .
%Y A225832 A225910 is the table of (m,n)-rectangular grids.
%K A225832 nonn,easy
%O A225832 0,2
%A A225832 _Yosu Yurramendi_, May 16 2013