A225834 Number of binary pattern classes in the (10,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, 528, 262912, 268713984, 274878693376, 281475261923328, 288230376957018112, 295147905471410601984, 302231454904481927397376, 309485009821644135887536128, 316912650057058194799105933312, 324518553658427033027930681769984, 332306998946228969090642893525221376

Offset: 0

Author

Yosu Yurramendi, May 16 2013

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (1024,1024,-1048576).

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.

Programs

Magma

[2^(5*n-3)*(2^(5*n+1)-(2^5-1)*(-1)^n+2^5+5): n in [0..20]]; // Vincenzo Librandi, Sep 04 2013

Mathematica

CoefficientList[Series[(1 - 496 x - 278784 x^2) / ((1 - 32 x) (1 + 32 x) (1 - 1024 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Sep 04 2013 *)

Formula

a(n) = 2^10*a(n-1) + 2^10*a(n-2) - (2^10)^2*a(n-3), with n>2 , a(0)=1, a(1)=528, a(2)=262912.

a(n) = 2^(5n-3)*(2^(5n+1)-(2^5-1)*(-1)^n+2^5+5).

G.f.: (1-496*x-278784*x^2)/((1-32*x)*(1+32*x)*(1-1024*x)).