Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #14 Jan 14 2021 18:17:13
%S 0,1,3,5,10,13,20,25,34,41,52,61,74,85,100,113,130,145,164,181,202,
%T 221,244,265,290,313,340,365,394,421,452,481,514,545,580,613,650,685,
%U 724,761,802,841,884,925,970,1013,1060,1105,1154,1201,1252,1301,1354,1405,1460,1513
%N Radio number of the path graph P_n.
%C a(n) is also the largest possible radio number for a graph on n nodes.
%H D. D.-F. Liu and X. Zhu, <a href="http://www.math.nsysu.edu.tw/~zhu/papers/labeling/SIAM-RadioDec-05Z.pdf">Multilevel Distance Labelings for Paths and Cycles</a>, SIAM J. Disc. Math. 19, 610-621, 2005.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PathGraph.html">Path Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RadioNumber.html">Radio Number</a>
%F a(n) = A236283(n-1) for n > 1, n != 3.
%F a(n) = 0 for n = 1,
%F = 3 for n = 3,
%F = (n - 2)*n/2 + 1 for n even,
%F = (n - 3)*(n + 1)/2 + 4 for n odd.
%F G.f.: x^2*(1 + x^2)*(1 + x - 2*x^2 + x^3)/((1 - x)^3*(1 + x)).
%Y Cf. A236283.
%K nonn
%O 1,3
%A _Eric W. Weisstein_, Jan 10 2021