A349417 - OEIS

%I #17 Dec 18 2021 23:45:55

%S 9,18,32,52,79,114,158,212,277,354,444,548,667,802,954,1124,1313,1522,

%T 1752,2004,2279,2578,2902,3252,3629,4034,4468,4932,5427,5954,6514,

%U 7108,7737,8402,9104,9844,10623,11442,12302,13204,14149,15138,16172,17252,18379,19554,20778

%N a(n) is the Wiener index of a sling on n+1 vertices.

%C A sling on n+1 vertices is a caterpillar that is obtained by adding 1 pendant vertex to the first (or last) internal vertex of a path on n >= 3 vertices.

%F a(n) = n^3/6 + n^2/2 - 2n/3 + 2.

%e For n=3, a(3)=9 gives the Wiener index of a star graph on 4 vertices. For n=4, a(4)=18 gives the Wiener index of a sling graph on 5 vertices.

%e    *

%e *__\*__*__*

%t Table[n^3/6 + n^2/2 - 2n/3 + 2, {n, 3, 102}]

%Y Cf. A349416 (broom), A349418 (tridon).

%Y Essentially same as A005581(n)+2.

%K nonn,look

%O 3,1

%A _Julian Allagan_, Nov 16 2021