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A370769
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Number of achiral unicursal star polygons (no edge joins adjacent vertices) that can be formed by connecting the vertices of a regular n-gon.
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2
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0, 0, 0, 0, 1, 1, 5, 11, 49, 123, 521, 1583, 6581, 23239, 95509, 384771, 1570265, 7106995, 28869825, 145034327, 587270877, 3242792607, 13100475021, 78866628011, 318067071169, 2073381189259, 8350998470777, 58602568320255, 235794888434053, 1772311322357623
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OFFSET
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1,7
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COMMENTS
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Achiral means that the polygon has an axis of reflective symmetry.
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LINKS
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FORMULA
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PROG
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(PARI)
Ro(n)=-(-1)^n + subst(serlaplace(polcoef(((1 - x)^2)/(2*(1 + x)*(1 + (1 - 2*y)*x + 2*y*x^2)) + O(x*x^n), n)), y, 1)
Re(n)=subst(serlaplace(polcoef((1 - 3*x)/(8*(1 + (1 - 2*y)*x + 2*y*x^2)) + O(x*x^n), n)), y, 1)
a(n) = if(n < 3, 0, if(n % 2, Ro(n\2), Re(n/2)))
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CROSSREFS
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Cf. A231091 (stars up to rotation), A370459 (up to rotation and reflection).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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