A371154 - OEIS

%I #23 Apr 05 2024 00:37:32

%S 1,3,5,8,11,16,21,26,33,40,47,56,65,74,85,96,107,120,133,146,161,176,

%T 191,208,225,242,261,280,299,320,341,362,385,408,431,456,481,506,533,

%U 560,587

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

%H M. A. Fiol, J. L. A. Yebra, I. Alegre, and M. Valero <a href="https://doi.org/10.1109/TC.1987.1676963"> Discrete optimization problem in local networks and data alignment</a>, IEEE Trans. Comput., C-36 (1987), no. 6, 702-713.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1).

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

%F G.f.: (1 + x - x^4 + 2*x^5 - x^6)/((1 - x)^3*(1 + x + x^2)). - _Stefano Spezia_, Mar 13 2024

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

%t 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 *)

%Y Essentially A008810 - 1.

%K nonn,easy

%O 0,2

%A _Miquel A. Fiol_, Mar 13 2024