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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. 8
1, 10, 76, 1120, 16576, 263680, 4197376, 67133440, 1073790976, 17180262400, 274878693376, 4398052802560, 70368756760576, 1125900007505920, 18014398710808576, 288230377762324480, 4611686021648613376, 73786976320608010240, 1180591620768950910976, 18889465931890897715200 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 7 13:27 EDT 2020. Contains 333305 sequences. (Running on oeis4.)