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A132390 Number of binary pattern classes in the (2,n)-rectangular grid; two patterns are in same class if one of them can be obtained by reflection or rotation of the other one. 2
3, 6, 24, 76, 288, 1072, 4224, 16576, 66048, 262912, 1050624, 4197376, 16785408, 67121152, 268468224, 1073790976, 4295098368, 17180065792, 68720001024, 274878693376, 1099513724928, 4398049656832, 17592194433024, 70368756760576 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A005418 is the solution for the problem in the (1,n)-rectangular grid.

For n != 2, a(n) = 4^(n-1) + 2*A133572(n-1). - Jon E. Schoenfield, Aug 25 2009

A225826 is the same sequence, except a(2)=7. Here, 90-degree rotation is allowed, so a(2)=6. [Yosu Yurramendi, May 18 2013 - communicated by Jon E. Schoenfield]

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,4,-16).

FORMULA

For n != 2, a(n) = 4^(n-1) + 2^(n-2)*(3 + (n mod 2)). - Jon E. Schoenfield, Aug 25 2009

From Colin Barker, May 20 2013: (Start)

a(n) = 2^(-3+n)*(7 - (-1)^n + 2^(1+n)) for n > 2.

a(n) = 4*a(n-1) + 4*a(n-2) - 16*a(n-3), n >= 6.

G.f.: -x*(16*x^4 - 4*x^3 + 12*x^2 + 6*x - 3) / ((2*x-1)*(2*x+1)*(4*x-1)). (End)

MATHEMATICA

CoefficientList[Series[-(16 x^4 - 4 x^3 + 12 x^2 + 6 x - 3) / ((2 x - 1) (2 x + 1) (4 x - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Sep 04 2013 *)

LinearRecurrence[{4, 4, -16}, {3, 6, 24, 76, 288}, 30] (* Harvey P. Dale, Sep 22 2016 *)

PROG

(MAGMA) I:=[3, 6, 24, 76, 288]; [n le 5 select I[n] else 4*Self(n-1)+4*Self(n-2)-16*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Sep 04 2013

CROSSREFS

Cf. A005418, A034851.

Sequence in context: A148656 A279300 A054718 * A327643 A296215 A152761

Adjacent sequences:  A132387 A132388 A132389 * A132391 A132392 A132393

KEYWORD

nonn,easy

AUTHOR

Yosu Yurramendi, Aug 26 2008

EXTENSIONS

More terms from Jon E. Schoenfield, Aug 25 2009, corrected Aug 30 2009

STATUS

approved

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)