A181688 Number of maximal self-avoiding walks from NW to SW corners of a 4-by-n grid.

1, 1, 4, 8, 23, 55, 144, 360, 921, 2329, 5924, 15024, 38159, 96847, 245888, 624176, 1584593, 4022609, 10211940, 25924088, 65811431, 167069767, 424126160, 1076693080, 2733310377, 6938824361, 17615009476, 44717740000, 113521160607, 288186606623

Offset: 1

Author

Sean A. Irvine, Nov 17 2010

Keywords

• nonn
• walk

Examples

			Illustration of a(1)=a(2)=1:
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Illustration of a(3)=4:
   .__.__.    .  .__.    .  .__.    .__.__.
   .__.__|    |__|  |    |  |  |    .__.  |
   |__.__.    .__.  |    |__|  |    |  |  |
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Links

• Index entries for linear recurrences with constant coefficients, signature (2, 2, -2, 1).

Crossrefs

Row 4 of A271592.

Cf. A000532, A014524, A014523, A181689, A003695, A006864.

Programs

Mathematica

LinearRecurrence[{2, 2, -2, 1}, {1, 1, 4, 8}, 30] (* T. D. Noe, Nov 06 2013 *)

Formula

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

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

Extensions

G.f. formula reverted to the original (correct) value by Stefan Bühler, Nov 06 2013