A349418 a(n) is the Wiener index of a tridon on n vertices.

16, 28, 46, 71, 104, 146, 198, 261, 336, 424, 526, 643, 776, 926, 1094, 1281, 1488, 1716, 1966, 2239, 2536, 2858, 3206, 3581, 3984, 4416, 4878, 5371, 5896, 6454, 7046, 7673, 8336, 9036, 9774, 10551, 11368, 12226, 13126, 14069, 15056, 16088, 17166, 18291, 19464, 20686

Offset: 5

Author

Julian Allagan, Nov 16 2021

Keywords

• nonn
• easy

Comments

A tridon on n vertices is a caterpillar that is obtained by adding 2 distinct pendant vertices to the first (or last) internal vertex of a path on n >= 3 vertices.

Examples

			For n=5, a(5)=16 gives the Wiener index of a star graph on 5 vertices. Also, for n=6, a(6)=28 gives the Wiener index of a tridon graph on 6 vertices.
    *
*____\*____*____*
     /
    *
		

Crossrefs

Cf. A349416 (broom), A349417 (sling).

Programs

Mathematica

Table[(1/6)*n^3 - (19/6)*n + 11, {n, 1, 100}]

Formula

a(n) = (1/6)*n^3 - (19/6)*n + 11.