login
A140662
Number of possible column states for self-avoiding polygons in a slit of width n.
2
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
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
Column k=2 of A203717 (shifted).
Sequence in context: A026582 A187003 A101893 * A174198 A077997 A294407
KEYWORD
easy,nonn
AUTHOR
R. J. Mathar, Jul 11 2008
STATUS
approved