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A300850
Number of 6-cycles in the n-odd graph.
0
0, 0, 10, 105, 840, 5775, 36036, 210210, 1166880, 6235515, 32332300, 163601438, 811246800, 3954828150, 19001896200, 90162058500, 423160594560, 1967035576275, 9066060164700, 41468830753350, 188390256054000, 850582006083810, 3818939619151800, 17058982348359900
OFFSET
1,3
LINKS
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, Odd Graph
FORMULA
a(n) = binomial(2*n-1, n-1)*n*(n-1)^2/12 for n > 2. - Andrew Howroyd, Mar 13 2018
From Robert Israel, Mar 13 2018: (Start)
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)
MAPLE
0, 0, seq(binomial(2*n-1, n-1)*n*(n-1)^2/12, n=3..40); # Robert Israel, Mar 13 2018
MATHEMATICA
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}]]
PROG
(PARI) a(n)={if(n==2, 0, binomial(2*n-1, n-1)*n*(n-1)^2/12)} \\ Andrew Howroyd, Mar 13 2018
CROSSREFS
Sequence in context: A117833 A117832 A268763 * A360276 A210136 A068093
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Mar 13 2018
EXTENSIONS
Terms a(8) and beyond from Andrew Howroyd, Mar 13 2018
STATUS
approved