OFFSET
6,1
LINKS
Andrew Howroyd, Table of n, a(n) for n = 6..1000
Julian D. Allagan, Enumeration and asymptotic analysis of edge-disjoint triangle packings in complete graphs, Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 128, 3-30, 2025. See p. 17.
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
a(n) = 120*binomial(n, 6) + 735*binomial(n, 7) + 840*binomial(n, 8) + 280*binomial(n, 9).
G.f.: 5*x^6*(24 + 75*x - 54*x^2 + 11*x^3)/(1 - x)^10.
EXAMPLE
a(6) = 120 gives the number of triples of edge-disjoint triangles in K_6.
MATHEMATICA
a[n_] := 120*Binomial[n, 6] + 735*Binomial[n, 7] + 840*Binomial[n, 8] + 280*Binomial[n, 9];
sequenceValues = Table[a[n], {n, 6, 30}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Julian Allagan, Mar 08 2025
STATUS
approved