

A360937


Triangle read by rows: T(n, k) is the kth LieBetti 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
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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



PROG

(SageMath) # uses[betti_numbers, LieAlgebraFromGraph from A360571]
return betti_numbers(LieAlgebraFromGraph(graphs.WheelGraph(n)))
for n in range(3, 7): print(A360937_row(n))


CROSSREFS



KEYWORD

nonn,tabf


AUTHOR



STATUS

approved



