A054557 Number of labeled pure 2-complexes on n nodes (0-simplexes) with 5 2-simplexes and 10 1-simplexes.

72, 4824, 32256, 127008, 378000, 940464, 2062368, 4115232, 7629336, 13333320, 22198176, 35485632, 54800928, 82149984, 120000960, 171350208, 239792616, 329596344, 445781952, 594205920, 781648560, 1015906320, 1305888480, 1661718240, 2094838200, 2618120232

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=10.

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

• Vincenzo Librandi, Table of n, a(n) for n = 5..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Programs

Magma

I:=[72, 4824, 32256, 127008, 378000, 940464, 2062368]; [n le 7 select I[n] else 7*Self(n-1)-21*Self(n-2)+35*Self(n-3)-35*Self(n-4)+21*Self(n-5)-7*Self(n-6)+Self(n-7): n in [1..25]]; // Vincenzo Librandi, Apr 28 2012

Mathematica

CoefficientList[Series[72*(1+60*x)/(1-x)^7,{x,0,30}],x] (* Vincenzo Librandi, Apr 28 2012 *)

Formula

a(n) = 72*C(n, 5)+4392*C(n, 6) = n*(n-1)*(n-2)*(n-3)*(n-4)*(61*n-299)/10.

G.f.: 72*x^5*(1+60*x)/(1-x)^7. - Colin Barker, Jan 19 2012

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7). Vincenzo Librandi, Apr 28 2012

Extensions

More terms from James Sellers, Apr 11 2000