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A362007
Fourth Lie-Betti number of a path graph on n vertices.
3
0, 0, 3, 16, 48, 107, 203, 347, 551, 828, 1192, 1658, 2242, 2961, 3833, 4877, 6113, 7562, 9246, 11188, 13412, 15943, 18807, 22031, 25643, 29672, 34148, 39102, 44566, 50573, 57157, 64353, 72197, 80726, 89978, 99992, 110808
OFFSET
1,3
COMMENTS
Sequence T(n,4) in A360571.
LINKS
Marco Aldi and Samuel Bevins, L_oo-algebras and hypergraphs, arXiv:2212.13608 [math.CO], 2022. See page 9.
Meera Mainkar, Graphs and two step nilpotent Lie algebras, arXiv:1310.3414 [math.DG], 2013. See page 1.
Eric Weisstein's World of Mathematics, Path Graph.
FORMULA
a(1) = a(2) = 0, a(3) = 3, a(n) = (n^4 + 18*n^3 - 97*n^2 + 174*n - 168)/24 for n >= 4.
a(n) = A011379(n-3) + A006002(n-4) + A001105(n-3) + A056106(n-2) + A000027(n-3) + A000332(n-3) + A000217(n-5) + A000027(n-4) for n >= 5.
PROG
(Python)
def A362007(n):
values = [0, 0, 3]
for i in range(4, n+1):
result = (i**4 + 18*i**3 - 97*i**2 + 174*i - 168)/24
values.append(int(result))
return values
CROSSREFS
Cf. A360571 (path graph triangle), A088459 (second Lie-Betti number of path graphs), A361230.
Sequence in context: A296947 A255211 A172482 * A212564 A222843 A346556
KEYWORD
nonn
AUTHOR
Samuel J. Bevins, Apr 05 2023
EXTENSIONS
a(34) and Python program corrected by Robert C. Lyons, Apr 17 2023
STATUS
approved