A038579 Number of self-avoiding closed walks from 0 of area n in strip Z X {0,1,2}.

1, 4, 10, 28, 64, 140, 304, 640, 1326, 2716, 5502, 11052, 22044, 43700, 86180, 169184, 330810, 644564, 1251954, 2424860, 4684696, 9029756, 17368408, 33343520, 63899686, 122259372, 233568998, 445600236, 849014964, 1615709156, 3071307852

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• walk
• easy

References

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

Links

• Index entries for linear recurrences with constant coefficients, signature (2,1,0,-3,-2,-1).

Crossrefs

Cf. A022445, A038578.

Programs

Mathematica

CoefficientList[ Series[(2 + 4 x^3 + 4 x^4)/(1 - x - x^2 - x^3)^2 - 1, {x, 0, 28}], x]
LinearRecurrence[{2, 1, 0, -3, -2, -1}, {1, 4, 10, 28, 64, 140, 304}, 31] (* Robert P. P. McKone, Jan 28 2021, same method used in A038578 MMA *)

PARI

Vec(2*(1+2*x^3+2*x^4)/(1-x-x^2-x^3)^2-1+ O(x^40)) \\ Michel Marcus, Jan 28 2021

Formula

G.f.: 2(1+2x^3+2x^4)/(1-x-x^2-x^3)^2-1 [Labelle]. - Emeric Deutsch, Apr 29 2004

Extensions

More terms from Emeric Deutsch, Apr 29 2004