A181689 Number of maximal self-avoiding walks from NW to SW corners of a 5 X n grid.

1, 0, 8, 0, 86, 0, 948, 0, 10444, 0, 115056, 0, 1267512, 0, 13963520, 0, 153828832, 0, 1694652176, 0, 18669100976, 0, 205667768400, 0, 2265734756752, 0, 24960420526224, 0, 274975961325264, 0, 3029267044091408, 0, 33371858326057936, 0, 367640393509287824, 0, 4050102862690348880, 0, 44617875206245953552, 0, 491531908055724064720, 0, 5414951194338345409680, 0, 59653698888134291413584, 0, 657173751585588653678864, 0, 7239741169830151881286864

Offset: 1

Author

Sean A. Irvine, Nov 17 2010

Keywords

• nonn
• easy
• walk

Comments

All even terms are 0.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,11,0,0,0,2).

Crossrefs

Row 5 of A271592.

Cf. A000532, A003778, A006865, A014584, A014585, A181688.

Programs

Magma

I:=[1,0,8,0,86,0]; [n le 6 select I[n] else 11*Self(n-2)+2*Self(n-6): n in [1..50]]; // Wesley Ivan Hurt, Apr 10 2016

Maple

A181689:=proc(n) option remember:
if n mod 2 = 0 then 0 elif n=1 then 1 elif n=3 then 8 elif n=5 then 86 else 11*a(n-2)+2*a(n-6); fi; end: seq(A181689(n), n=1..50); # Wesley Ivan Hurt, Apr 10 2016

Mathematica

CoefficientList[Series[(1 - 3*x^2 - 2*x^4)/(1 - 11*x^2 - 2*x^6), {x, 0, 50}], x] (* Wesley Ivan Hurt, Apr 10 2016 *)

PARI

x='x+O('x^99); Vec(x*(1-3*x^2-2*x^4)/(1-11*x^2-2*x^6)) \\ Altug Alkan, Apr 11 2016

Formula

G.f.: x*(1 - 3*x^2 - 2*x^4)/(1 - 11*x^2 - 2*x^6).

a(n) = 11*a(n-2) + 2*a(n-6) for n>6. - Wesley Ivan Hurt, Apr 10 2016