A340528 - 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