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 180-degree rotation of the other.

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

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(n-1) + 16*a(n-2) - (16^2)*a(n-3) with n>2, a(0)=1, a(1)=10, a(2)=76.

a(n) = 2^(2n-3)*(2^(2n+1)-3*(-1)^n+9).

G.f.: (1-6*x-100*x^2)/((1-4*x)*(1+4*x)*(1-16*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(n-1)+16*Self(n-2)-256*Self(n-3): 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