A381863 Number of triples of triangles that are pairwise edge-disjoint in the complete graph K_n.

120, 1575, 10080, 44380, 154000, 451990, 1170400, 2748460, 5965960, 12137125, 23383360, 43006600, 75988640, 129645740, 214472000, 345209480, 542187800, 832980995, 1254434720, 1855122500, 2698295600, 3865397250, 5460218400, 7613778900, 10490025000

Offset: 6

Author

Julian Allagan, Mar 08 2025

Keywords

• nonn
• easy

Examples

			a(6) = 120 gives the number of triples of edge-disjoint triangles in K_6.
		

References

• Julian Allagan, Edge-Disjoint Triangle Packings in Complete Graphs: Recurrence Relations and Closed Formulas. A revised proof version is to submitted to a Journal.

Links

• Andrew Howroyd, Table of n, a(n) for n = 6..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Cf. A381862, A054647.

Programs

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}]

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.