

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
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OFFSET

1,1


COMMENTS

A005418 is the solution for the problem in the (1,n)rectangular grid.
For n != 2, a(n) = 4^(n1) + 2*A133572(n1).  Jon E. Schoenfield, Aug 25 2009
A225826 is the same sequence, except a(2)=7. Here, 90degree 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^(n1) + 2^(n2)*(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(n1) + 4*a(n2)  16*a(n3), n >= 6.
G.f.: x*(16*x^4  4*x^3 + 12*x^2 + 6*x  3) / ((2*x1)*(2*x+1)*(4*x1)). (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(n1)+4*Self(n2)16*Self(n3): 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



