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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. 6
1, 36, 1072, 66816, 4197376, 268517376, 17180065792, 1099516870656, 70368756760576, 4503599962914816, 288230376957018112, 18446744095184388096, 1180591620768950910976, 75557863727288712953856, 4835703278461815233708032, 309485009821433029655003136, 19807040628566295504618520576, 1267650600228235030996237418496 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 3 04:21 EDT 2020. Contains 333195 sequences. (Running on oeis4.)