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

4,1

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).

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

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 *)

Prog

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

Crossrefs

Cf. A054563.

Sequence in context: A284764 A271421 A064204 * A006434 A240397 A347425

Adjacent sequences: A054641 A054642 A054643 * A054645 A054646 A054647

Keyword

nonn,easy

Author

Vladeta Jovovic, Apr 15 2000

Extensions

More terms from James A. Sellers, Apr 16 2000

Status

approved