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A225826 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 a reflection or 180-degree rotation of the other. 22

%I

%S 1,3,7,24,76,288,1072,4224,16576,66048,262912,1050624,4197376,

%T 16785408,67121152,268468224,1073790976,4295098368,17180065792,

%U 68720001024,274878693376,1099513724928,4398049656832,17592194433024,70368756760576

%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 a reflection or 180-degree rotation of the other.

%H Vincenzo Librandi, <a href="/A225826/b225826.txt">Table of n, a(n) for n = 0..1000</a>

%H Gregory Emmett Coxson and Jon Carmelo Russo, <a href="https://dx.doi.org/10.1109/TAES.2017.2675238">Enumeration and Generation of PSL Equivalence Classes for Quad-Phase Codes of Even Length</a>, IEEE Transactions on Aerospace and Electronic Systems, Year: 2017, Volume: 53, Issue: 4, p. 1907-1915.

%H Vincent Pilaud, V Pons, <a href="http://arxiv.org/abs/1606.09643">Permutrees</a>, arXiv preprint arXiv:1606.09643 [math.CO], 2016.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,4,-16).

%F a(n) = 4*a(n-1) + 4*a(n-2)- 16*a(n-3) with n>2, a(0)=1, a(1)=3, a(2)=7 (communicated by _Jon E. Schoenfield_).

%F a(n) = 2^(n-3)*(2^(n+1)-(-1)^n+7).

%F G.f.: (1-x-9*x^2)/((1-2*x)*(1+2*x)*(1-4*x)).

%t LinearRecurrence[{4, 4, -16}, {1, 3, 7}, 30] (* _Bruno Berselli_, May 17 2013 *)

%t CoefficientList[Series[(1 - x - 9 x^2) / ((1 - 2 x) (1 + 2 x) (1 - 4 x)), {x, 0, 33}], x] (* _Vincenzo Librandi_, Sep 03 2013 *)

%o (MAGMA) [2^(n-3)*(2^(n+1)-(-1)^n+7): n in [0..25]]; // _Vincenzo Librandi_, Sep 03 2013

%Y Cf. A005418 = Number of binary pattern classes in the (1,n)-rectangular grid, A225826 to A225834 are the numbers of binary pattern classes in the (m,n)-rectangular grid, 1 < m < 11, A132390 is the sequence when the 90 degree rotation for pattern equivalence is allowed. So, only a(2) is different (communicated by Jon E. Schoenfield). See A054247 for (n,n)-grids.

%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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Last modified December 7 20:33 EST 2019. Contains 329849 sequences. (Running on oeis4.)