A054648 Number of labeled pure 2-complexes on n nodes (0-simplexes) with 4 2-simplexes and 11 1-simplexes.

360, 13230, 137760, 835380, 3679200, 13056120, 39584160, 106383420, 259819560, 586936350, 1242521280, 2489618040, 4758324480, 8728907040, 15446635200, 26477304840, 44114190120, 71649152190, 113722852320, 176771479500, 269590120800, 404035889400, 595897192800

Offset: 6

Author

Vladeta Jovovic, Apr 16 2000

Keywords

• nonn

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=11.

References

• 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

Crossrefs

Cf. A054557-A054562.

Formula

a(n) = 360*C(n, 6)+10710*C(n, 7)+42000*C(n, 8)+41580*C(n, 9)+12600*C(n, 10) = n*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n^4+3*n^3-58*n^2-120*n+1008)/288.

Empirical G.f.: -30*x^6*(89*x^4-391*x^3+401*x^2+309*x+12)/(x-1)^11. [Colin Barker, Jun 22 2012]

Extensions

More terms from James Sellers, Apr 16 2000