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%I #33 Sep 08 2022 08:46:05
%S 1,136,16576,4212736,1073790976,274882625536,70368756760576,
%T 18014399717441536,4611686021648613376,1180591621026648948736,
%U 302231454904481927397376,77371252455415432018395136,19807040628566295504618520576
%N 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 Vincenzo Librandi, <a href="/A225832/b225832.txt">Table of n, a(n) for n = 0..400</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (256,256,-65536).
%F 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 a(n) = 2^(4n-3)*(2^(4n+1)-(2^4-1)*(-1)^n+2^4+5).
%F G.f.: (1-120*x-18496*x^2)/((1-16*x)*(1+16*x)*(1-256*x)).
%t 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 (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 A005418 is the number of binary pattern classes in the (1,n)-rectangular grid.
%Y A225826 to A225834 are the numbers of binary pattern classes in the (m,n)-rectangular grid, 1 < m < 11 .
%Y A225910 is the table of (m,n)-rectangular grids.
%K nonn,easy
%O 0,2
%A _Yosu Yurramendi_, May 16 2013
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