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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. 4
1, 136, 16576, 4212736, 1073790976, 274882625536, 70368756760576, 18014399717441536, 4611686021648613376, 1180591621026648948736, 302231454904481927397376, 77371252455415432018395136, 19807040628566295504618520576 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 10 05:04 EDT 2020. Contains 333392 sequences. (Running on oeis4.)