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A283847
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Number of n-gonal inositol homologs with 2 kinds of achiral proligands.
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9
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2, 8, 36, 140, 522, 1920, 7030, 25704, 94302, 347488, 1286460, 4785300, 17879352, 67076096, 252579600, 954306220, 3616552422, 13743371072, 52356648380, 199909107900, 764873459802, 2932022620160, 11258982291252
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OFFSET
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3,1
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LINKS
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FORMULA
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From Robert Israel, Aug 23 2018 after Fujita (2017), Eq. (100)(set n=2, m=n): (Start)
if n is even, a(n) = (4*n)^(-1)*(Sum_{d|n, d odd} phi(d)*4^(n/d) - 2^(n-1).
if n is odd, a(n) = (4*n)^(-1)*Sum_{d|n} phi(d)*4^(n/d) - 2^(n-1). (End)
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MAPLE
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f:= proc(n) uses numtheory;
if n::even then (4*n)^(-1)*add(phi(d)*4^(n/d), d = select(type, divisors(n), odd)) - 2^(n-1)
else (4*n)^(-1)*add(phi(d)*4^(n/d), d = divisors(n)) - 2^(n-1)
fi
end proc:
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MATHEMATICA
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a[n_] := If[EvenQ[n], (4n)^(-1) Sum[EulerPhi[d] 4^(n/d), {d, Select[ Divisors[n], OddQ]}] - 2^(n-1), (4n)^(-1) Sum[EulerPhi[d] 4^(n/d), {d, Divisors[n]}] - 2^(n-1)];
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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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