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A360572
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Triangle read by rows: T(n,k) is the k-th Lie-Betti number of the cycle graph on n vertices, n >= 3, 0 <= k <= 2*n.
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8
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1, 3, 8, 12, 8, 3, 1, 1, 4, 14, 25, 28, 25, 14, 4, 1, 1, 5, 20, 41, 70, 90, 70, 41, 20, 5, 1, 1, 6, 27, 68, 146, 219, 238, 219, 146, 68, 27, 6, 1, 1, 7, 35, 105, 259, 449, 644, 756, 644, 449, 259, 105, 35, 7, 1, 1, 8, 44, 152, 422, 857, 1476, 2012, 2172, 2012, 1476, 857, 422, 152, 44, 8, 1
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OFFSET
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3,2
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LINKS
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EXAMPLE
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Triangle 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 14 25 28 25 14 4 1
n=5 1 5 20 41 70 90 70 41 20 5 1
n=6 1 6 27 68 146 219 238 219 146 68 27 6 1
n=7 1 7 35 105 259 449 644 756 644 449 259 105 35 7 1
n=8 1 8 44 152 422 857 1476 2012 2172 2012 1476 857 422 152 44 8 1
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PROG
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(SageMath) # uses[betti_numbers, LieAlgebraFromGraph from A360571]
return betti_numbers(LieAlgebraFromGraph(graphs.CycleGraph(n)))
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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