cp's OEIS Frontend

A364579 Fifth Lie-Betti number of a path graph on n vertices.

%I A364579 #14 Feb 16 2025 08:34:06
%S A364579 0,0,1,11,48,140,329,668,1223,2074,3316,5060,7434,10584,14675,19892,
%T A364579 26441,34550,44470,56476,70868,87972,108141,131756,159227,190994,
%U A364579 227528,269332,316942,370928,431895,500484,577373,663278,758954
%N A364579 Fifth Lie-Betti number of a path graph on n vertices.
%C A364579 Sequence T(n,5) in A360571.
%H A364579 Marco Aldi and Samuel 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 A364579 Meera 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 A364579 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PathGraph.html">Path Graph</a>.
%F A364579 a(1) = a(2) = 0, a(3) = 1, a(4) = 11, a(n) = (n^5 + 30*n^4 - 145*n^3 - 270*n^2 + 2424*n - 3360)/120 for n >= 5.
%o A364579 (Python)
%o A364579 def A364579_up_to(n):
%o A364579     values = [0, 0, 1, 11]
%o A364579     for i in range(5, n+1):
%o A364579         result = (i**5 + 30*i**4 - 145*i**3 - 270*i**2 + 2424*i - 3360)/120
%o A364579         values.append(int(result))
%o A364579     return values
%Y A364579 Cf. A360571 (path graph triangle), A088459 (second Lie-Betti number of path graphs), A361230, A362007.
%K A364579 nonn
%O A364579 1,4
%A A364579 _Samuel J. Bevins_, Aug 14 2023