A140662 Number of possible column states for self-avoiding polygons in a slit of width n.

1, 3, 8, 20, 50, 126, 322, 834, 2187, 5797, 15510, 41834, 113633, 310571, 853466, 2356778, 6536381, 18199283, 50852018, 142547558, 400763222, 1129760414, 3192727796, 9043402500, 25669818475, 73007772801, 208023278208

Offset

1,2

Comments

Number of Dyck (n+1)-paths whose maximum ascent length is 2. - David Scambler, Aug 22 2012

Links

Table of n, a(n) for n=1..27.

J. Alvarez, E.J. Janse van Rensburg et al. Self-avoiding walks and polygons in slits.

Louis Marin, Counting Polyominoes in a Rectangle b X h, arXiv:2406.16413 [cs.DM], 2024. See p. 148.

Formula

a(n) = Sum_{m=1..[(n+1)/2]} (n+1)!/((n+1-2m)!m!(m+1)!).

a(n) = A001006(n+2)-1.

D-finite with recurrence (n+3)*a(n) +(-4*n-7)*a(n-1) +(2*n+3)*a(n-2) +(4*n-5) *a(n-3) +3*(-n+2)*a(n-4)=0. - R. J. Mathar, Nov 01 2021

Crossrefs

Cf. A055151, A080159, A088617, A107131, A097610.

Column k=2 of A203717 (shifted).

Sequence in context: A026582 A187003 A101893 * A174198 A077997 A294407

Adjacent sequences: A140659 A140660 A140661 * A140663 A140664 A140665

Keyword

easy,nonn

Author

R. J. Mathar, Jul 11 2008

Status

approved