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 A132390 Number of binary pattern classes in the (2,n)-rectangular grid; two patterns are in same class if one of them can be obtained by reflexion or rotation of the other one. 1

%I

%S 3,6,24,76,288,1072,4224,16576,66048,262912,1050624,4197376,16785408,

%T 67121152,268468224,1073790976,4295098368,17180065792,68720001024,

%U 274878693376,1099513724928,4398049656832,17592194433024,70368756760576

%N Number of binary pattern classes in the (2,n)-rectangular grid; two patterns are in same class if one of them can be obtained by reflexion or rotation of the other one.

%C A005418 is the solution for the problem in the (1,n)-rectangular grid

%C For n<>2, a(n)=4^(n-1)+2*A133572(n-1). [From Jon E. Schoenfield (jonscho(AT)hiwaay.net), Aug 25 2009]

%C A225826 is the same sequence, except a(2)=7. Here, 90-degree rotation is allowed, so a(2)=6. [_Yosu Yurramendi_, May 18 2013 - communicated by Jon E. Schoenfield).

%H <a href="/index/Rea#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (4,4,-16).

%F For n<>2, a(n)=4^(n-1)+2^(n-2)*(3+(n mod 2)). [From Jon E. Schoenfield (jonscho(AT)hiwaay.net), Aug 25 2009]

%F a(n) = 2^(-3+n)*(7-(-1)^n+2^(1+n)) for n>2. a(n) = 4*a(n-1)+4*a(n-2)-16*a(n-3). G.f.: -x*(16*x^4-4*x^3+12*x^2+6*x-3) / ((2*x-1)*(2*x+1)*(4*x-1)). - _Colin Barker_, May 20 2013

%Y Cf. A005418, A034851.

%K nonn,easy,changed

%O 1,1

%A Yosu Yurramendi (yosu.yurramendi(AT)ehu.es), Aug 26 2008

%E More terms from Jon E. Schoenfield (jonscho(AT)hiwaay.net), Aug 25 2009, corrected Aug 30 2009

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