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A112945
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Number of unrooted regular odd-valent planar maps with 4 vertices; maps are considered up to orientation-preserving homeomorphisms and the vertices are of valency 2n+1.
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3
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0, 6, 468, 80600, 16016560, 3360790440, 728936019504, 161858688461184, 36580777518027600, 8382066029146609800, 1941971956789550319920, 454006489072843947528288, 106944132919124515725427808
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = (n/6)*binomial(2n, n)^4+(n/2)*binomial(2n, n)^2+(2/3)*delta(3|(2n+1))* binomial(2*floor(n/3), floor(n/3))*binomial(2n, n) where delta(3|(2n+1))=1 if 3|(2n+1) and =0 otherwise.
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MATHEMATICA
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a[n_] := (n/6) Binomial[2n, n]^4 + (n/2) Binomial[2n, n]^2 + (2/3) Boole[ Divisible[2n+1, 3]] Binomial[2 Floor[n/3], Floor[n/3]] Binomial[2n, n];
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CROSSREFS
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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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