A349417 -id:A349417 - cp's OEIS frontend

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

Julian Allagan, Nov 16 2021

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.

			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).
  *     *
   \   /
*__ \*/___*___*
    / \
   /   \
  *     *

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

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

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

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

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

Original entry on oeis.org

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

Julian Allagan, Nov 16 2021

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.

			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.
    *
*____\*____*____*
     /
    *

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

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

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

cp's OEIS Frontend

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

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