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%I #26 Sep 08 2022 08:46:05
%S 1,528,262912,268713984,274878693376,281475261923328,
%T 288230376957018112,295147905471410601984,302231454904481927397376,
%U 309485009821644135887536128,316912650057058194799105933312,324518553658427033027930681769984,332306998946228969090642893525221376
%N Number of binary pattern classes in the (10,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="/A225834/b225834.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1024,1024,-1048576).
%F a(n) = 2^10*a(n-1) + 2^10*a(n-2) - (2^10)^2*a(n-3), with n>2 , a(0)=1, a(1)=528, a(2)=262912.
%F a(n) = 2^(5n-3)*(2^(5n+1)-(2^5-1)*(-1)^n+2^5+5).
%F G.f.: (1-496*x-278784*x^2)/((1-32*x)*(1+32*x)*(1-1024*x)).
%t CoefficientList[Series[(1 - 496 x - 278784 x^2) / ((1 - 32 x) (1 + 32 x) (1 - 1024 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Sep 04 2013 *)
%o (Magma) [2^(5*n-3)*(2^(5*n+1)-(2^5-1)*(-1)^n+2^5+5): n in [0..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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