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.

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

Offset: 3

Author

Samuel J. Bevins, Feb 26 2023

Keywords

• nonn
• tabf

Examples

			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

• 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.

Crossrefs

Cf. A360571 (path graph), A360572 (cycle graph), A088459 (star graph), A360625 (complete graph), A360936 (ladder graph), A361044 (friendship graph).

Programs

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))