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A360572 Triangle read by rows: T(n,k) is the k-th Lie-Betti number of the cycle graph on n vertices, n >= 3, 0 <= k <= 2*n. 8
1, 3, 8, 12, 8, 3, 1, 1, 4, 14, 25, 28, 25, 14, 4, 1, 1, 5, 20, 41, 70, 90, 70, 41, 20, 5, 1, 1, 6, 27, 68, 146, 219, 238, 219, 146, 68, 27, 6, 1, 1, 7, 35, 105, 259, 449, 644, 756, 644, 449, 259, 105, 35, 7, 1, 1, 8, 44, 152, 422, 857, 1476, 2012, 2172, 2012, 1476, 857, 422, 152, 44, 8, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,2
LINKS
M. Aldi and S. Bevins, L_oo-algebras and hypergraphs, arXiv:2212.13608 [math.CO], 2022. See page 9.
M. Mainkar, Graphs and two step nilpotent Lie algebras, arXiv:1310.3414 [math.DG], 2013. See page 1.
Eric Weisstein's World of Mathematics, Cycle Graph.
EXAMPLE
Triangle begins:
k=0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
n=3 1 3 8 12 8 3 1
n=4 1 4 14 25 28 25 14 4 1
n=5 1 5 20 41 70 90 70 41 20 5 1
n=6 1 6 27 68 146 219 238 219 146 68 27 6 1
n=7 1 7 35 105 259 449 644 756 644 449 259 105 35 7 1
n=8 1 8 44 152 422 857 1476 2012 2172 2012 1476 857 422 152 44 8 1
...
PROG
(SageMath) # uses[betti_numbers, LieAlgebraFromGraph from A360571]
def A360936(n):
return betti_numbers(LieAlgebraFromGraph(graphs.CycleGraph(n)))
CROSSREFS
Cf. A360571 (path graph), A088459 (star graph), A360625 (complete graph), A360936 (ladder graph), A360937 (wheel graph)
Sequence in context: A201882 A356865 A050391 * A360937 A361044 A288865
KEYWORD
nonn,tabf
AUTHOR
Samuel J. Bevins, Feb 12 2023
STATUS
approved

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Last modified February 21 07:54 EST 2024. Contains 370219 sequences. (Running on oeis4.)