

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 180degree rotation of the other.


22



1, 3, 7, 24, 76, 288, 1072, 4224, 16576, 66048, 262912, 1050624, 4197376, 16785408, 67121152, 268468224, 1073790976, 4295098368, 17180065792, 68720001024, 274878693376, 1099513724928, 4398049656832, 17592194433024, 70368756760576
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OFFSET

0,2


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Gregory Emmett Coxson and Jon Carmelo Russo, Enumeration and Generation of PSL Equivalence Classes for QuadPhase Codes of Even Length, IEEE Transactions on Aerospace and Electronic Systems, Year: 2017, Volume: 53, Issue: 4, p. 19071915.
Vincent Pilaud, V Pons, Permutrees, arXiv preprint arXiv:1606.09643 [math.CO], 2016.
Index entries for linear recurrences with constant coefficients, signature (4,4,16).


FORMULA

a(n) = 4*a(n1) + 4*a(n2) 16*a(n3) with n>2, a(0)=1, a(1)=3, a(2)=7 (communicated by Jon E. Schoenfield).
a(n) = 2^(n3)*(2^(n+1)(1)^n+7).
G.f.: (1x9*x^2)/((12*x)*(1+2*x)*(14*x)).


MATHEMATICA

LinearRecurrence[{4, 4, 16}, {1, 3, 7}, 30] (* Bruno Berselli, May 17 2013 *)
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 *)


PROG

(MAGMA) [2^(n3)*(2^(n+1)(1)^n+7): n in [0..25]]; // Vincenzo Librandi, Sep 03 2013


CROSSREFS

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.
A225910 is the table of (m,n)rectangular grids.
Sequence in context: A138541 A290750 A148720 * A228992 A246657 A038169
Adjacent sequences: A225823 A225824 A225825 * A225827 A225828 A225829


KEYWORD

nonn,easy


AUTHOR

Yosu Yurramendi, May 16 2013


STATUS

approved



