A225832 Number of binary pattern classes in the (8,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, 136, 16576, 4212736, 1073790976, 274882625536, 70368756760576, 18014399717441536, 4611686021648613376, 1180591621026648948736, 302231454904481927397376, 77371252455415432018395136, 19807040628566295504618520576

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..400

Index entries for linear recurrences with constant coefficients, signature (256,256,-65536).

Formula

a(n) = 2^8*a(n-1) + 2^8*a(n-2) - (2^8)^2*a(n-3), with n>2, a(0)=1, a(1)=136, a(2)=16576.

a(n) = 2^(4n-3)*(2^(4n+1)-(2^4-1)*(-1)^n+2^4+5).

G.f.: (1-120*x-18496*x^2)/((1-16*x)*(1+16*x)*(1-256*x)).

Mathematica

CoefficientList[Series[(1 - 120 x - 18496 x^2) / ((1 - 16 x) (1 + 16 x) (1 - 256 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Sep 04 2013 *)

Prog

(Magma) I:=[1, 136, 16576]; [n le 3 select I[n] else 256*Self(n-1)+256*Self(n-2)-65536*Self(n-3): n in [1..20]]; // 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: A035819 A233086 A278185 * A233172 A233127 A157880

Adjacent sequences: A225829 A225830 A225831 * A225833 A225834 A225835

Keyword

nonn,easy

Author

Yosu Yurramendi, May 16 2013

Status

approved