A349416 a(n) is the Wiener index of a broom on 2n vertices of which n+2 are pendant.

25, 54, 100, 167, 259, 380, 534, 725, 957, 1234, 1560, 1939, 2375, 2872, 3434, 4065, 4769, 5550, 6412, 7359, 8395, 9524, 10750, 12077, 13509, 15050, 16704, 18475, 20367, 22384, 24530, 26809, 29225, 31782, 34484, 37335, 40339, 43500, 46822, 50309, 53965, 57794, 61800, 65987

Offset: 3

Author

Julian Allagan, Nov 16 2021

Keywords

• nonn
• easy

Comments

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

Examples

			For n=3 the value a(3)=25 gives the Wiener index of a star graph on 6 vertices. For n=4, a(4)=54 gives the Wiener index of a broom graph on 8 vertices (6 of which are leaves).
  *     *
   \   /
*__ \*/___*___*
    / \
   /   \
  *     *
		

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A349417 (sling), A349418 (tridon).

Programs

Mathematica

nterms=50;Table[2n^3/3+n^2/2+5n/6,{n,3,nterms+2}] (* Paolo Xausa, Nov 22 2021 *)

Formula

a(n) = 2n^3/3 + n^2/2 + 5n/6.