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URL: https://oeis.org/A349416

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A349416
a(n) is the Wiener index of a broom on 2n vertices of which n+2 are pendant.
2
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
3,1
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.
FORMULA
a(n) = 2n^3/3 + n^2/2 + 5n/6.
EXAMPLE
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).
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MATHEMATICA
nterms=50; Table[2n^3/3+n^2/2+5n/6, {n, 3, nterms+2}] (* Paolo Xausa, Nov 22 2021 *)
CROSSREFS
Cf. A349417 (sling), A349418 (tridon).
Sequence in context: A117472 A146633 A123825 * A157269 A371129 A186892
KEYWORD
nonn,easy
AUTHOR
Julian Allagan, Nov 16 2021
STATUS
approved