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A231091
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Number of distinct (modulo rotation) unicursal star polygons (not necessarily regular, no edge joins adjacent vertices) that can be formed by connecting the vertices of a regular n-gon.
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5
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0, 0, 0, 0, 1, 1, 5, 27, 175, 1533, 14361, 151575, 1735869, 21594863, 289365383, 4158887007, 63822480809, 1041820050629, 18027531255745, 329658402237171, 6352776451924233, 128686951765990343, 2733851297673484765, 60781108703102022027, 1411481990523638719737
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OFFSET
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1,7
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COMMENTS
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LINKS
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FORMULA
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EXAMPLE
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For n=5, only solution is the regular pentagram.
For n=6, only solution is the unicursal hexagram (see Wikipedia link).
For n=7, two regular heptagrams and three irregular forms are possible.
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PROG
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b(n)={subst(serlaplace(polcoef((1 - x)/(1 + (1 - 2*y)*x + 2*y*x^2) + O(x*x^n), n)), y, 1)}
a(n)={(if(n%2==0 && n > 2, b(n/2-1)/2) + a370068(n))/2} \\ Andrew Howroyd, Mar 01 2024
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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