A054558 Number of labeled pure 2-complexes on n nodes (0-simplexes) with 5 2-simplexes and 9 1-simplexes.

150, 960, 3605, 10360, 25200, 54600, 108570, 201960, 356070, 600600, 975975, 1536080, 2351440, 3512880, 5135700, 7364400, 10377990, 14395920, 19684665, 26565000, 35420000, 46703800, 60951150, 78787800, 100941750, 128255400

Offset: 5

Author

Vladeta Jovovic, Apr 10 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=5, l=9.

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

• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A054557.

Programs

Maple

A054558:=n->n*(n-1)*(n-2)*(n-3)*(n-4)*(n^2+n+150)/144; seq(A054558(n), n=5..30); # Wesley Ivan Hurt, Apr 29 2014

Mathematica

Table[n*(n - 1)*(n - 2)*(n - 3)*(n - 4)*(n^2 + n + 150)/144, {n, 5, 30}] (* Wesley Ivan Hurt, Apr 29 2014 *)

Formula

a(n) = 150*C(n,5) +60*C(n,6) +35*C(n,7) = n*(n-1)*(n-2)*(n-3)*(n-4)*(n^2+n+150)/144.

G.f.: 5*x^5*(30-48*x+25*x^2)/(1-x)^8. - Colin Barker, Jun 21 2012