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
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