%I #9 Apr 11 2024 10:04:21
%S 1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,7,7,7,7,8,8,8,8,9,9,9,9,
%T 10,10,10,10,11,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,15,15,15,
%U 15,16,16,16,16,17,17,17,17,18,18,18,18,19,19,19,19,20,20,20,20,21,21,21
%N Diameter of a special type of regular graph of degree 4 whose order maintain an increase in form of an arithmetic progression.
%D Claude C.S. and Dinneen M.J (1998), Group-theoretic methods for designing networks, Discrete mathematics and theoretical computer science, Research report
%D Comellas, F. and Gomez, J. (1995), New large graphs with given degree and diameter, in Proceedings of the seventh quadrennial international conference on the theory and applications of graphs, Volume 1: pp. 222-233
%D Ibrahim, A., A. (2007), A stable variety of Cayley graphs (in preparation)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphThickness.html">Graph Thickness</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 1, -1).
%F f(D4,5)=1: Order =4,5; f(D)= f(D4,5)+n: order=5+n, n=1,2,...
%F I am assuming this sequence is just Floor[(n+5)/4]... [From _Eric W. Weisstein_, Sep 09 2008]
%e f(D4,5)=1 when order=4, f(D4,5)=1 when order=5, f(D)=f(D4,5)+1=1+1=2 when order is 5+1=6
%Y Cf. A123642.
%Y First differences of A186347.
%K nonn
%O 4,3
%A _Aminu Alhaji Ibrahim_, Apr 25 2007