A054644 Number of labeled pure 2-complexes on n nodes with 3 2-simplexes.

4, 120, 1140, 6545, 27720, 95284, 280840, 735130, 1750540, 3858140, 7971964, 15596035, 29112720, 52174360, 90223760, 151173044, 246274580, 391222160, 607525380, 924205205, 1379864024, 2025189100, 2925954200, 4166590350

Offset: 4

Author

Vladeta Jovovic, Apr 15 2000

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 4..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Cf. A054563.

Programs

Magma

[n*(n-1)*(n-2)*(n-3)*(n^2+2)*(n^3-3*n^2+2*n-12)/1296: n in [4..30]]; // Vincenzo Librandi, Apr 30 2012

Mathematica

Table[Binomial[Binomial[n,3],3],{n,4,60}] (* Vladimir Joseph Stephan Orlovsky, May 30 2010 *)
LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{4,120,1140,6545,27720,95284,280840,735130,1750540,3858140},30] (* Vincenzo Librandi, Apr 30 2012 *)

Sage

[(binomial(binomial(n,3),3)) for n in range(4, 28)] # Zerinvary Lajos, Nov 30 2009

Formula

a(n) = binomial(binomial(n, 3), 3) = 4*binomial(n, 4) + 100*binomial(n, 5) + 480*binomial(n, 6) + 945*binomial(n, 7) + 840*binomial(n, 8) + 280*binomial(n, 9) = n*(n-1)*(n-2)*(n-3)*(n^2+2)*(n^3 - 3*n^2 + 2*n - 12)/1296.

G.f.: x^4*(4 + 80*x + 120*x^2 + 65*x^3 + 10*x^4 + x^5)/(1-x)^10. - Colin Barker, Jan 19 2012

Extensions

More terms from James Sellers, Apr 16 2000