A355645 The number of regions in the G-Shi arrangement when G is the cycle graph C_n.

1, 3, 16, 61, 206, 659, 2052, 6297, 19162, 58015, 175088, 527333, 1586118, 4766571, 14316124, 42981169, 129009074, 387158327, 1161737160, 3485735805, 10458256030, 31376865283, 94134790196, 282412759241, 847255054986, 2541798719439, 7625463267232

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.

Links

Table of n, a(n) for n=1..27.

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

Crossrefs

Cf. A004146 (cycle graph labels).

Cf. A000244 (path graph regions), A001906 (path graph labels).

Sequence in context: A259056 A155160 A370305 * A323941 A267036 A037451

Adjacent sequences: A355642 A355643 A355644 * A355646 A355647 A355648

Keyword

nonn,easy

Author

Robin Truax, Jul 11 2022

Status

approved