OFFSET
1,2
COMMENTS
The G-Shi arrangement of a graph G is the hyperplane arrangement given by hyperplanes x_i - x_j = 0 and x_i - x_j = 1 for each edge {i,j} of G with i < j.
a(n) is also the number of parking functions of length n with all cars preferring to park in the first 3 spots. - Jayden Thadani, May 20 2024
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..1000
Douglas M. Chen, On the Structure of Permutation Invariant Parking, arXiv:2311.15699 [math.CO], 2023. See p. 16.
Index entries for linear recurrences with constant coefficients, signature (7,-17,17,-6).
FORMULA
a(n) = 3^n - 2^n - n for n >= 2.
G.f.: x*(1 - 4*x + 12*x^2 - 17*x^3 + 6*x^4)/((1 - x)^2*(1 - 2*x)*(1 - 3*x)). - Stefano Spezia, Jul 12 2022
MATHEMATICA
LinearRecurrence[{7, -17, 17, -6}, {1, 3, 16, 61, 206}, 50] (* Paolo Xausa, May 24 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robin Truax, Jul 11 2022
STATUS
approved