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.

1, 20, 288, 8640, 263680, 8407040, 268517376, 8590786560, 274882625536, 8796137062400, 281475261923328, 9007201737768960, 288230393868451840, 9223372185031147520, 295147906296044322816, 9444732974878980833280, 302231454974575793668096, 9671406557490978467348480

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 A329710 A125477

Adjacent sequences: A225826 A225827 A225828 * A225830 A225831 A225832

Keyword

nonn,easy

Author

Yosu Yurramendi, May 16 2013

Status

approved