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A225829 Number of binary pattern classes in the (5,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. 7
1, 20, 288, 8640, 263680, 8407040, 268517376, 8590786560, 274882625536, 8796137062400, 281475261923328, 9007201737768960, 288230393868451840, 9223372185031147520, 295147906296044322816, 9444732974878980833280, 302231454974575793668096, 9671406557490978467348480 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..600

Index entries for linear recurrences with constant coefficients, signature (40,-224,-1280,8192).

FORMULA

a(n) = 32*a(n-1) + 32*a(n-2) - 1024*a(n-3)- 2^(3n - 3)*3 with n>2, a(0)=1, a(1)=20, a(2)=288.

a(n) = 2^(5n/2-1)*(2^(5n/2-1) + 2^(n/2-1) + 1) if n is even,

a(n) = 2^((5n-1)/2-1)*(2^((5n-1)/2) + 2^((n-1)/2) + 5) if n is odd.

G.f.: (1-20*x-288*x^2+2880*x^3)/((1-8*x)*(1-32*x)*(1-32*x^2)). [Bruno Berselli, May 17 2013]

MATHEMATICA

LinearRecurrence[{40, -224, -1280, 8192}, {1, 20, 288, 8640}, 20] (* Bruno Berselli, May 17 2013 *)

CoefficientList[Series[(1 - 20 x - 288 x^2 + 2880 x^3) / ((1 - 8 x) (1 - 32 x) (1 - 32 x^2)), {x, 0, 30}], x] (* Vincenzo Librandi, Sep 04 2013 *)

PROG

(MAGMA) I:=[1, 20, 288, 8640]; [n le 4 select I[n] else 40*Self(n-1)-224*Self(n-2)-1280*Self(n-3)+8192*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Sep 04 2013

CROSSREFS

A005418 is the 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 .

A225910 is the table of (m,n)-rectangular grids.

Sequence in context: A231105 A016314 A021164 * A017918 A125477 A016261

Adjacent sequences:  A225826 A225827 A225828 * A225830 A225831 A225832

KEYWORD

nonn,easy

AUTHOR

Yosu Yurramendi, May 16 2013

STATUS

approved

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Last modified November 14 22:32 EST 2019. Contains 329134 sequences. (Running on oeis4.)