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A300850
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Number of 6-cycles in the n-odd graph.
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0
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0, 0, 10, 105, 840, 5775, 36036, 210210, 1166880, 6235515, 32332300, 163601438, 811246800, 3954828150, 19001896200, 90162058500, 423160594560, 1967035576275, 9066060164700, 41468830753350, 188390256054000, 850582006083810, 3818939619151800, 17058982348359900
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OFFSET
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1,3
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LINKS
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Eric Weisstein's World of Mathematics, Odd Graph
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FORMULA
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a(n) = binomial(2*n-1, n-1)*n*(n-1)^2/12 for n > 2. - Andrew Howroyd, Mar 13 2018
G.f.: x^2*(1+6*x)/(2*(1-4*x)^(7/2))-x^2/2.
(12+24*n)*a(n)+(22-2*n)*a(n+1)-n*a(n+2)=0. (End)
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MAPLE
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0, 0, seq(binomial(2*n-1, n-1)*n*(n-1)^2/12, n=3..40); # Robert Israel, Mar 13 2018
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MATHEMATICA
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Join[{0, 0}, Table[Binomial[2 n - 1, n - 1] n (n - 1)^2/12, {n, 3, 18}]]
CoefficientList[Series[x (1/(1 - 4 x)^(7/2) + (6 x)/(1 - 4 x)^(7/2) - 1)/2, {x, 0, 20}], x]
Join[{0, 0}, RecurrenceTable[{(12 + 24 n) a[n] + (22 - 2 n) a[n + 1] == n a[n + 2], a[3] == 10, a[4] == 105}, a, {n, 3, 20}]]
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PROG
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(PARI) a(n)={if(n==2, 0, binomial(2*n-1, n-1)*n*(n-1)^2/12)} \\ Andrew Howroyd, Mar 13 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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