A225830 Number of binary pattern classes in the (6,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, 36, 1072, 66816, 4197376, 268517376, 17180065792, 1099516870656, 70368756760576, 4503599962914816, 288230376957018112, 18446744095184388096, 1180591620768950910976, 75557863727288712953856, 4835703278461815233708032, 309485009821433029655003136, 19807040628566295504618520576, 1267650600228235030996237418496

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (64,64,-4096).

Formula

a(n) = 64*a(n-1) + 64*a(n-2) - (64^2)*a(n-3) with n>2, a(0)=1, a(1)=36, a(2)=1072.

a(n) = 2^(3n-3)*(2^(3n+1)-(2^3-1)*(-1)^n+2^3+5) = 8^(n-1)*(2^(3n+1)-7*(-1)^n+13).

G.f.: (1-28*x-1296*x^2)/((1-8*x)*(1+8*x)*(1-64*x)).

Mathematica

LinearRecurrence[{64, 64, -4096}, {1, 36, 1072}, 20] (* Bruno Berselli, May 17 2013 *)
CoefficientList[Series[(1 - 28 x - 1296 x^2) / ((1 - 8 x) (1 + 8 x) (1 - 64 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Sep 04 2013 *)

Prog

(Magma) I:=[1, 36, 1072]; [n le 3 select I[n] else 64*Self(n-1)+64*Self(n-2)-4096*Self(n-3): 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: A180802 A223358 A184292 * A000809 A151584 A233085

Adjacent sequences: A225827 A225828 A225829 * A225831 A225832 A225833

Keyword

nonn,easy

Author

Yosu Yurramendi, May 16 2013

Status

approved