A371154 Maximum number of vertices for a given diameter n of a Cayley digraph on the cyclic group with generators s=1 and t>s.

1, 3, 5, 8, 11, 16, 21, 26, 33, 40, 47, 56, 65, 74, 85, 96, 107, 120, 133, 146, 161, 176, 191, 208, 225, 242, 261, 280, 299, 320, 341, 362, 385, 408, 431, 456, 481, 506, 533, 560, 587

Offset

0,2

Links

Table of n, a(n) for n=0..40.

M. A. Fiol, J. L. A. Yebra, I. Alegre, and M. Valero Discrete optimization problem in local networks and data alignment, IEEE Trans. Comput., C-36 (1987), no. 6, 702-713.

Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).

Formula

a(n) = ceiling((n+2)^2/3)-1 for n<>1.

G.f.: (1 + x - x^4 + 2*x^5 - x^6)/((1 - x)^3*(1 + x + x^2)). - Stefano Spezia, Mar 13 2024

Example

For n=10, the maximum number of vertices a(n)=47 is obtained, for instance, with the Cayley digraph Cay(47;1,11).

Mathematica

CoefficientList[Series[(1 + x - x^4 + 2*x^5 - x^6)/((1 - x)^3*(1 + x + x^2)), {x, 0, 40}], x] (* or *) Join[{1, 3}, Table[Ceiling[(n+2)^2/3]-1, {n, 2, 40}]] (* James C. McMahon, Apr 04 2024 *)

Crossrefs

Essentially A008810 - 1.

Sequence in context: A099836 A344010 A281333 * A338204 A244031 A194803

Adjacent sequences: A371151 A371152 A371153 * A371155 A371156 A371157

Keyword

nonn,easy

Author

Miquel A. Fiol, Mar 13 2024

Status

approved