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.

3, 6, 24, 76, 288, 1072, 4224, 16576, 66048, 262912, 1050624, 4197376, 16785408, 67121152, 268468224, 1073790976, 4295098368, 17180065792, 68720001024, 274878693376, 1099513724928, 4398049656832, 17592194433024, 70368756760576

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 * A363016 A327643 A296215

Adjacent sequences: A132387 A132388 A132389 * A132391 A132392 A132393

Keyword

nonn,easy,changed

Author

Yosu Yurramendi, Aug 26 2008

Extensions

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

Status

approved