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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
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 (list; graph; refs; listen; history; text; internal format)
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 Quad-Phase Codes of Even Length, IEEE Transactions on Aerospace and Electronic Systems, Year: 2017, Volume: 53, Issue: 4, p. 1907-1915.

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(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).

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

G.f.: (1-x-9*x^2)/((1-2*x)*(1+2*x)*(1-4*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^(n-3)*(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

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Last modified February 23 07:06 EST 2018. Contains 299473 sequences. (Running on oeis4.)