A054647 Number of labeled pure 2-complexes on n nodes (0-simplexes) with 4 2-simplexes and 12 1-simplexes.

30, 2310, 42840, 391545, 2375100, 10980585, 41761720, 136963255, 399689290, 1060984925, 2603641040, 5979294230, 12973080120, 26794003110, 53000811600, 100914240770, 185718969590, 331524753560, 575738427880, 975199600375, 1614655942900, 2618302433175

Offset: 6

Author

Vladeta Jovovic, Apr 16 2000

Keywords

• nonn
• easy

Comments

Number of {T_1,T_2,...,T_k} where T_i,i=1..k are 3-subsets of an n-set such that {D | D is 2-subset of T_i for some i=1..k} has l elements; k=4,l=12.

Numbers of sets of 4 triangles that are pairwise edge-disjoint in the complete graph K_n. - Julian Allagan, Mar 08 2025

References

• Julian Allagan, Edge-Disjoint Triangle Packings in Complete Graphs: Recurrence Relations and Closed Formulas (submitted 2025)
• V. Jovovic, On the number of two-dimensional simplicial complexes (in Russian), Metody i sistemy tekhnicheskoy diagnostiki, Vypusk 16, Mezhvuzovskiy zbornik nauchnykh trudov, Izdatelstvo Saratovskogo universiteta, 1991.

Links

• T. D. Noe, Table of n, a(n) for n = 6..1000
• Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Crossrefs

Cf. A054557, A054558, A054559, A054560, A054561, A054562, A381862, A381863.

Formula

a(n) = 30*C(n, 6)+2100*C(n, 7)+25200*C(n, 8)+86625*C(n, 9)+116550*C(n, 10)+69300*C(n, 11)+15400*C(n, 12) = n*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n^6+3*n^5-86*n^4-240*n^3+2704*n^2+5232*n-34128)/31104.

G.f.: 5*x^6*(169*x^6-1119*x^5+2535*x^4-1245*x^3-3030*x^2-384*x-6)/(x-1)^13. [Colin Barker, Jun 22 2012]

Extensions

More terms from James Sellers, Apr 16 2000