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A361014 Triangle read by rows: T(n,k) is the k-th Lie-Betti number of the hypercube graph on 2^(n-1) vertices, n >= 1, k >= 0.

%I A361014 #15 Feb 28 2023 18:16:24
%S A361014 1,1,1,2,2,1,1,4,14,25,28,25,14,4,1,1,8,64,258,986,2870,6134,11586,
%T A361014 18830,23832,25078,23832,18830,11586,6134,2870,986,258,64,8,1
%N A361014 Triangle read by rows: T(n,k) is the k-th Lie-Betti number of the hypercube graph on 2^(n-1) vertices, n >= 1, k >= 0.
%H A361014 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 A361014 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 A361014 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HypercubeGraph.html">Hypercube Graph</a>.
%e A361014 Triangle begins:
%e A361014    k=0 1  2   3   4    5    6     7     8     9    10    11    12    13   14
%e A361014 n=1: 1 1
%e A361014 n=2: 1 2  2   1
%e A361014 n=3: 1 4 14  25  28   25   14     4     1
%e A361014 n=4: 1 8 64 258 986 2870 6134 11586 18830 23832 25078 23832 18830 11586 6134
%e A361014 ...
%o A361014 (SageMath) # uses[betti_numbers, LieAlgebraFromGraph from A360571]
%o A361014 def A360936_row(n):
%o A361014     if n == 1: return [1, 1]
%o A361014     return betti_numbers(LieAlgebraFromGraph(graphs.CubeGraph(n-1)))
%Y A361014 Cf. A360571 (path graph), A360572 (cycle graph), A088459 (star graph), A360625 (complete graph), A360936 (ladder graph), A360937 (wheel graph).
%K A361014 nonn,tabf,more
%O A361014 1,4
%A A361014 _Samuel J. Bevins_, Feb 28 2023