cp's OEIS Frontend

A363378 Third Lie-Betti number of a cycle graph on n vertices.

%I A363378 #20 Feb 16 2025 08:34:05
%S A363378 12,25,41,68,105,152,210,280,363,460,572,700,845,1008,1190,1392,1615,
%T A363378 1860,2128,2420,2737,3080,3450,3848,4275,4732,5220,5740,6293,6880,
%U A363378 7502,8160,8855,9588,10360,11172,12025,12920,13858
%N A363378 Third Lie-Betti number of a cycle graph on n vertices.
%C A363378 Sequence T(n,3) in A360572.
%H A363378 M. Aldi and S. Bevins, <a href="https://arxiv.org/abs/2212.13608">L_oo-algebras and hypergraphs</a>, arXiv:2212.13608 [math.CO], 2022. See page 9.
%H A363378 M. Mainkar, <a href="https://arxiv.org/abs/1310.3414">Graphs and two step nilpotent Lie algebras</a>, arXiv:1310.3414 [math.DG], 2013. See page 1.
%H A363378 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CycleGraph.html">Cycle Graph</a>.
%F A363378 a(3) = 12, a(4) = 25, a(5) = 41, a(n) = n*(n+11)*(n-2)/6 for n >= 6.
%F A363378 a(n) = A005581(n-4) + A054000(n-1) + A028347(n-2) + A000027(n) for n >= 6.
%F A363378 a(n) = A106058(n+1) - 2 for n >= 6. - _Hugo Pfoertner_, Jun 02 2023
%o A363378 (Python)
%o A363378 def A363378(n):
%o A363378     values = [12,25,41]
%o A363378     for i in range(6, n+1):
%o A363378         result = (i*(i+11)*(i-2))/6
%o A363378         values.append(result)
%o A363378     return values
%Y A363378 Cf. A005581, A054000, A028347, A000027, A360572 (cycle graph triangle)
%K A363378 nonn
%O A363378 3,1
%A A363378 _Samuel J. Bevins_, Jun 01 2023