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A364946
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Sixth Lie-Betti number of a path graph on n vertices.
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0
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0, 0, 0, 4, 33, 140, 424, 1039, 2213, 4262, 7606, 12786, 20482, 31532, 46952, 67957, 95983, 132710, 180086, 240352, 316068, 410140, 525848, 666875, 837337, 1041814, 1285382, 1573646, 1912774, 2309532, 2771320, 3306209, 3922979, 4631158, 5441062
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listen;
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OFFSET
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1,4
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COMMENTS
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LINKS
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Eric Weisstein's World of Mathematics, Path Graph.
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FORMULA
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a(1) = a(2) = a(3) = 0, a(4) = 4, a(5) = 33, a(n) = (n^6 + 45*n^5 - 125*n^4 - 2865*n^3 + 23524*n^2 - 76740*n + 98640)/720 for n >= 6.
G.f.: x^4*(4 + 5*x - 7*x^2 - 3*x^3 - 4*x^4 + 15*x^5 - 15*x^6 + 7*x^7 - x^8)/(1 - x)^7. - Stefano Spezia, Aug 29 2023
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PROG
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(Python)
values = [0, 0, 0, 4, 33]
for i in range(6, n+1):
result = (i**6 + 45*i**5 - 125*i**4 - 2865*i**3 + 23524*i**2 - 76740*i + 98640)/720
values.append(int(result))
return values
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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