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A360936 Triangle read by rows: T(n,k) is the k-th Lie-Betti number of the ladder graph on 2*n vertices, n >= 2, k >= 0.

%I A360936 #21 May 04 2024 09:23:43
%S A360936 1,2,2,1,1,4,14,25,28,25,14,4,1,1,6,32,89,204,357,437,437,357,204,89,
%T A360936 32,6,1,1,8,54,207,680,1650,3201,5310,6993,7508,6993,5310,3201,1650,
%U A360936 680,207,54,8,1
%N A360936 Triangle read by rows: T(n,k) is the k-th Lie-Betti number of the ladder graph on 2*n vertices, n >= 2, k >= 0.
%H A360936 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 A360936 Meera G. 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 A360936 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LadderGraph.html">Ladder Graph</a>.
%e A360936 Triangle begins:
%e A360936    k=0 1  2   3   4    5    6    7    8    9   10   11   12   13  14  15 16
%e A360936 n=1: 1 2  2   1
%e A360936 n=2: 1 4 14  25  28   25   14    4    1
%e A360936 n=3: 1 6 32  89 204  357  437  437  357  204   89   32    6    1
%e A360936 n=4: 1 8 54 207 680 1650 3201 5310 6993 7508 6993 5310 3201 1650 680 207 54
%e A360936 ...
%o A360936 (SageMath) # uses[betti_numbers, LieAlgebraFromGraph from A360571]
%o A360936 def A360936(n):
%o A360936     return betti_numbers(LieAlgebraFromGraph(graphs.LadderGraph(n)))
%Y A360936 Cf. A360571 (path graph), A360572 (cycle graph), A088459 (star graph), A360625 (complete graph), A360937 (wheel graph)
%K A360936 nonn,more,tabf
%O A360936 1,2
%A A360936 _Samuel J. Bevins_, Feb 26 2023