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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Essentially equal to A001006(n+2)-1, n>1.

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.

FORMULA

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

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

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Last modified September 25 00:48 EDT 2020. Contains 337333 sequences. (Running on oeis4.)