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A361230
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Third Lie-Betti number of a path graph on n vertices.
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4
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0, 1, 6, 16, 33, 58, 92, 136, 191, 258, 338, 432, 541, 666, 808, 968, 1147, 1346, 1566, 1808, 2073, 2362, 2676, 3016, 3383, 3778, 4202, 4656, 5141, 5658, 6208, 6792, 7411, 8066, 8758, 9488, 10257, 11066, 11916, 12808, 13743, 14722, 15746, 16816, 17933
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OFFSET
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1,3
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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) = 0, a(2) = 1, a(n) = (n^3 + 9*n^2 - 40*n + 48)/6 for n >= 3.
a(n) = [x^n] (x^2*(-x^4 + x^3 - 2*x^2 + 2*x + 1))/(x - 1)^4. - Peter Luschny, Mar 06 2023
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MAPLE
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gf := (x^2*(-x^4 + x^3 - 2*x^2 + 2*x + 1))/(x - 1)^4:
ser := series(gf, x, 50): seq(coeff(ser, x, n), n = 1..48); # Peter Luschny, Mar 06 2023
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PROG
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(Python)
values = [0, 1]
for i in range(3, n+1):
result = (i^3 + 9*i^2 - 40*i + 48)/6
values.append(result)
return values
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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