

A225828


Number of binary pattern classes in the (4,n)rectangular grid: two patterns are in the same class if one of them can be obtained by a reflection or 180degree rotation of the other.


8



1, 10, 76, 1120, 16576, 263680, 4197376, 67133440, 1073790976, 17180262400, 274878693376, 4398052802560, 70368756760576, 1125900007505920, 18014398710808576, 288230377762324480, 4611686021648613376, 73786976320608010240, 1180591620768950910976, 18889465931890897715200
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OFFSET

0,2


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..800
Index entries for linear recurrences with constant coefficients, signature (16,16,256).


FORMULA

a(n) = 16*a(n1) + 16*a(n2)  (16^2)*a(n3) with n>2, a(0)=1, a(1)=10, a(2)=76.
a(n) = 2^(2n3)*(2^(2n+1)3*(1)^n+9).
G.f.: (16*x100*x^2)/((14*x)*(1+4*x)*(116*x)). [Bruno Berselli, May 16 2013]


MATHEMATICA

Table[2^(2 n  3) (2^(2 n + 1)  3 (1)^n + 9), {n, 0, 20}] (* Bruno Berselli, May 16 2013 *)
LinearRecurrence[{16, 16, 256}, {1, 10, 76}, 20] (* Bruno Berselli, May 17 2013 *)
CoefficientList[Series[(1  6 x  100 x^2) / ((1  4 x) (1 + 4 x) (1  16 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Sep 04 2013 *)


PROG

(MAGMA) I:=[1, 10, 76]; [n le 3 select I[n] else 16*Self(n1)+16*Self(n2)256*Self(n3): n in [1..30]]; // 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: A075489 A184273 A185986 * A000808 A159579 A244720
Adjacent sequences: A225825 A225826 A225827 * A225829 A225830 A225831


KEYWORD

nonn,easy


AUTHOR

Yosu Yurramendi, May 16 2013


EXTENSIONS

More terms from Vincenzo Librandi, Sep 04 2013


STATUS

approved



