OFFSET
1,3
COMMENTS
Sequence T(n,4) in A360571.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..10000
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.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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.
From Stefano Spezia, Mar 02 2025: (Start)
G.f.: x^2*(3 + x - 2*x^2 - 3*x^3 + 3*x^4 - x^5)/(1 - x)^5.
E.g.f.: (12*(6 + 4*x + x^2) - exp(x)*(72 - 24*x - 36*x^2 - 28*x^3 - x^4))/24. (End)
MATHEMATICA
A362007[n_] := Which[n<=2, 0, n==3, 3, True, n*(n*(n*(n+18)-97)+174)/24-7]; Array[A362007, 50] (* or *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 3, 16, 48, 107, 203, 347}, 50] (* Paolo Xausa, Jan 23 2026 *)
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
KEYWORD
nonn,easy
AUTHOR
Samuel J. Bevins, Apr 05 2023
EXTENSIONS
a(34) and Python program corrected by Robert C. Lyons, Apr 17 2023
More terms from Paolo Xausa, Jan 23 2026
STATUS
approved
