A363378 - OEIS

%I #19 Jun 05 2023 09:29:57

%S 12,25,41,68,105,152,210,280,363,460,572,700,845,1008,1190,1392,1615,

%T 1860,2128,2420,2737,3080,3450,3848,4275,4732,5220,5740,6293,6880,

%U 7502,8160,8855,9588,10360,11172,12025,12920,13858

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

%C Sequence T(n,3) in A360572.

%H 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 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CycleGraph.html">Cycle Graph</a>.

%F a(3) = 12, a(4) = 25, a(5) = 41, a(n) = n*(n+11)*(n-2)/6 for n >= 6.

%F a(n) = A005581(n-4) + A054000(n-1) + A028347(n-2) + A000027(n) for n >= 6.

%F a(n) = A106058(n+1) - 2 for n >= 6. - _Hugo Pfoertner_, Jun 02 2023

%o (Python)

%o def A363378(n):

%o     values = [12,25,41]

%o     for i in range(6, n+1):

%o         result = (i*(i+11)*(i-2))/6

%o         values.append(result)

%o     return values

%Y Cf. A005581, A054000, A028347, A000027, A360572 (cycle graph triangle)

%K nonn

%O 3,1

%A _Samuel J. Bevins_, Jun 01 2023