A022444 Number of self-avoiding closed walks (from (0,0) to (0,0)) of length 2n in strip {-1, 0, 1} X Z.

1, 0, 8, 16, 44, 112, 252, 564, 1276, 2840, 6220, 13532, 29292, 63024, 134876, 287428, 610268, 1291336, 2724204, 5731500, 12029260, 25191008, 52646908, 109823636, 228707004, 475533432, 987305612, 2047088764, 4239132716

Offset: 0

Author

Jacques Labelle (labelle.jacques(AT)uqam.ca)

Keywords

• nonn
• walk
• easy

References

• J. Labelle, Self-avoiding walks and polyominoes in strips, Bull. ICA, 23 (1998), 88-98.

Links

• Sean A. Irvine, Java program (github)

Crossrefs

Cf. A007825, A022445.

Formula

G.f.: (-12*x^7+16*x^6-36*x^5+37*x^4-24*x^3+14*x^2-4*x+1) / ((1+x^2)^2*(1-2*x)^2) (conjectured).

Extensions

a(16)-a(28) and title improved by Sean A. Irvine, May 15 2019