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A140662
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Number of possible column states for self-avoiding polygons in a slit of width n.
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2
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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
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OFFSET
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1,2
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COMMENTS
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Number of Dyck (n+1)-paths whose maximum ascent length is 2. - David Scambler, Aug 22 2012
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LINKS
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FORMULA
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a(n) = Sum_{m=1..[(n+1)/2]} (n+1)!/((n+1-2m)!m!(m+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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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