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.

1, 2, 2, 1, 1, 4, 14, 25, 28, 25, 14, 4, 1, 1, 6, 32, 89, 204, 357, 437, 437, 357, 204, 89, 32, 6, 1, 1, 8, 54, 207, 680, 1650, 3201, 5310, 6993, 7508, 6993, 5310, 3201, 1650, 680, 207, 54, 8, 1

Offset

1,2

Links

Table of n, a(n) for n=1..46.

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, Ladder Graph.

Example

Triangle begins:
   k=0 1  2   3   4    5    6    7    8    9   10   11   12   13  14  15 16
n=1: 1 2  2   1
n=2: 1 4 14  25  28   25   14    4    1
n=3: 1 6 32  89 204  357  437  437  357  204   89   32    6    1
n=4: 1 8 54 207 680 1650 3201 5310 6993 7508 6993 5310 3201 1650 680 207 54
...

Prog

(SageMath) # uses[betti_numbers, LieAlgebraFromGraph from A360571]
def A360936(n):
    return betti_numbers(LieAlgebraFromGraph(graphs.LadderGraph(n)))

Crossrefs

Cf. A360571 (path graph), A360572 (cycle graph), A088459 (star graph), A360625 (complete graph), A360937 (wheel graph)

Sequence in context: A341991 A152937 A331315 * A361014 A064552 A209543

Adjacent sequences: A360933 A360934 A360935 * A360937 A360938 A360939

Keyword

nonn,more,tabf

Author

Samuel J. Bevins, Feb 26 2023

Status

approved