A340528 Radio number of the path graph P_n.

0, 1, 3, 5, 10, 13, 20, 25, 34, 41, 52, 61, 74, 85, 100, 113, 130, 145, 164, 181, 202, 221, 244, 265, 290, 313, 340, 365, 394, 421, 452, 481, 514, 545, 580, 613, 650, 685, 724, 761, 802, 841, 884, 925, 970, 1013, 1060, 1105, 1154, 1201, 1252, 1301, 1354, 1405, 1460, 1513

Offset: 1

Author

Eric W. Weisstein, Jan 10 2021

Keywords

• nonn

Comments

a(n) is also the largest possible radio number for a graph on n nodes.

Links

• D. D.-F. Liu and X. Zhu, Multilevel Distance Labelings for Paths and Cycles, SIAM J. Disc. Math. 19, 610-621, 2005.
• Eric Weisstein's World of Mathematics, Path Graph
• Eric Weisstein's World of Mathematics, Radio Number

Crossrefs

Cf. A236283.

Formula

a(n) = A236283(n-1) for n > 1, n != 3.

a(n) = 0 for n = 1,

= 3 for n = 3,

= (n - 2)*n/2 + 1 for n even,

= (n - 3)*(n + 1)/2 + 4 for n odd.

G.f.: x^2*(1 + x^2)*(1 + x - 2*x^2 + x^3)/((1 - x)^3*(1 + x)).