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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.
0
1, 1, 1, 2, 2, 1, 1, 4, 14, 25, 28, 25, 14, 4, 1, 1, 8, 64, 258, 986, 2870, 6134, 11586, 18830, 23832, 25078, 23832, 18830, 11586, 6134, 2870, 986, 258, 64, 8, 1
OFFSET
1,4
LINKS
Marco Aldi and Samuel Bevins, L_oo-algebras and hypergraphs, arXiv:2212.13608 [math.CO], 2022. See page 9.
Meera Mainkar, Graphs and two step nilpotent Lie algebras, arXiv:1310.3414 [math.DG], 2013. See page 1.
Eric Weisstein's World of Mathematics, Hypercube Graph.
EXAMPLE
Triangle begins:
k=0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
n=1: 1 1
n=2: 1 2 2 1
n=3: 1 4 14 25 28 25 14 4 1
n=4: 1 8 64 258 986 2870 6134 11586 18830 23832 25078 23832 18830 11586 6134
...
PROG
(SageMath) # uses[betti_numbers, LieAlgebraFromGraph from A360571]
def A360936_row(n):
if n == 1: return [1, 1]
return betti_numbers(LieAlgebraFromGraph(graphs.CubeGraph(n-1)))
CROSSREFS
Cf. A360571 (path graph), A360572 (cycle graph), A088459 (star graph), A360625 (complete graph), A360936 (ladder graph), A360937 (wheel graph).
Sequence in context: A152937 A331315 A360936 * A064552 A209543 A178655
KEYWORD
nonn,tabf,more
AUTHOR
Samuel J. Bevins, Feb 28 2023
STATUS
approved