cp's OEIS Frontend

A054647 Number of labeled pure 2-complexes on n nodes (0-simplexes) with 4 2-simplexes and 12 1-simplexes.

%I A054647 #20 Jul 02 2025 16:01:59
%S A054647 30,2310,42840,391545,2375100,10980585,41761720,136963255,399689290,
%T A054647 1060984925,2603641040,5979294230,12973080120,26794003110,53000811600,
%U A054647 100914240770,185718969590,331524753560,575738427880,975199600375,1614655942900,2618302433175
%N A054647 Number of labeled pure 2-complexes on n nodes (0-simplexes) with 4 2-simplexes and 12 1-simplexes.
%C A054647 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=12.
%C A054647 Numbers of sets of 4 triangles that are pairwise edge-disjoint in the complete graph K_n. - _Julian Allagan_, Mar 08 2025
%D A054647 Julian Allagan, Edge-Disjoint Triangle Packings in Complete Graphs: Recurrence Relations and Closed Formulas (submitted 2025)
%D A054647 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.
%H A054647 T. D. Noe, <a href="/A054647/b054647.txt">Table of n, a(n) for n = 6..1000</a>
%H A054647 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F A054647 a(n) = 30*C(n, 6)+2100*C(n, 7)+25200*C(n, 8)+86625*C(n, 9)+116550*C(n, 10)+69300*C(n, 11)+15400*C(n, 12) = n*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n^6+3*n^5-86*n^4-240*n^3+2704*n^2+5232*n-34128)/31104.
%F A054647 G.f.: 5*x^6*(169*x^6-1119*x^5+2535*x^4-1245*x^3-3030*x^2-384*x-6)/(x-1)^13. [_Colin Barker_, Jun 22 2012]
%Y A054647 Cf. A054557, A054558, A054559, A054560, A054561, A054562, A381862, A381863.
%K A054647 nonn,easy
%O A054647 6,1
%A A054647 _Vladeta Jovovic_, Apr 16 2000
%E A054647 More terms from _James Sellers_, Apr 16 2000