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%I #24 Dec 18 2021 23:47:16
%S 16,28,46,71,104,146,198,261,336,424,526,643,776,926,1094,1281,1488,
%T 1716,1966,2239,2536,2858,3206,3581,3984,4416,4878,5371,5896,6454,
%U 7046,7673,8336,9036,9774,10551,11368,12226,13126,14069,15056,16088,17166,18291,19464,20686
%N a(n) is the Wiener index of a tridon on n vertices.
%C 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.
%F a(n) = (1/6)*n^3 - (19/6)*n + 11.
%e 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.
%e *
%e *____\*____*____*
%e /
%e *
%t Table[(1/6)*n^3 - (19/6)*n + 11, {n, 1, 100}]
%Y Cf. A349416 (broom), A349417 (sling).
%K nonn,easy
%O 5,1
%A _Julian Allagan_, Nov 16 2021
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