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 A360937 Triangle read by rows: T(n, k) is the k-th Lie-Betti number of a wheel graph on n vertices, for n >= 3 and k >= 0. 5
 1, 3, 8, 12, 8, 3, 1, 1, 4, 20, 56, 84, 90, 84, 56, 20, 4, 1, 1, 5, 32, 108, 212, 371, 547, 547, 371, 212, 108, 32, 5, 1, 1, 6, 45, 171, 442, 1081, 2025, 2616, 2722, 2616, 2025, 1081, 442, 171, 45, 6, 1, 1, 7, 60, 258, 842, 2489, 5440, 8855, 12955, 16785, 16785, 12955, 8855, 5440, 2489, 842, 258, 60, 7, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 COMMENTS Triangle T(n, k) 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 20 56 84 90 84 56 20 4 1 n=5: 1 5 32 108 212 371 547 547 371 212 108 32 5 1 n=6: 1 6 45 171 442 1081 2025 2616 2722 2616 2025 1081 442 171 45 6 1 ... LINKS Table of n, a(n) for n=3..71. Marco Aldi and Samuel Bevins, L_oo-algebras and hypergraphs, arXiv:2212.13608 [math.CO], 2022. See page 9. Meera G. Mainkar, Graphs and two step nilpotent Lie algebras, arXiv:1310.3414 [math.DG], 2013. See page 1. Eric Weisstein's World of Mathematics, Wheel Graph. PROG (SageMath) # uses[betti_numbers, LieAlgebraFromGraph from A360571] def A360937_row(n): return betti_numbers(LieAlgebraFromGraph(graphs.WheelGraph(n))) for n in range(3, 7): print(A360937_row(n)) CROSSREFS Cf. A360571 (path graph), A360572 (cycle graph), A088459 (star graph), A360625 (complete graph), A360936 (ladder graph), A361044 (friendship graph). Sequence in context: A356865 A050391 A360572 * A361044 A288865 A331069 Adjacent sequences: A360934 A360935 A360936 * A360938 A360939 A360940 KEYWORD nonn,tabf AUTHOR Samuel J. Bevins, Feb 26 2023 STATUS approved

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Last modified December 6 19:52 EST 2023. Contains 367614 sequences. (Running on oeis4.)