A038578 Number of self-avoiding closed walks from 0 of area n in strip Z X {-1,0,1}.

1, 8, 16, 40, 88, 184, 388, 800, 1628, 3288, 6584, 13096, 25904, 50984, 99916, 195072, 379572, 736360, 1424672, 2749672, 5295240, 10176856, 19522644, 37387424, 71487756, 136492216, 260255304, 495618408, 942731360, 1791241544, 3399976348

Offset

0,2

References

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

Links

Table of n, a(n) for n=0..30.

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

Formula

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

Mathematica

LinearRecurrence[{2, 1, 0, -3, -2, -1}, {1, 8, 16, 40, 88, 184, 388}, 31] (* Georg Fischer, Jan 28 2021 *)

Prog

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

Crossrefs

Cf. A022444.

Sequence in context: A024700 A108576 A052207 * A348925 A155110 A245419

Adjacent sequences: A038575 A038576 A038577 * A038579 A038580 A038581

Keyword

nonn,walk,easy

Author

N. J. A. Sloane.

Extensions

More terms from Emeric Deutsch, Apr 29 2004

Status

approved