A349417 - OEIS

A349417

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

9, 18, 32, 52, 79, 114, 158, 212, 277, 354, 444, 548, 667, 802, 954, 1124, 1313, 1522, 1752, 2004, 2279, 2578, 2902, 3252, 3629, 4034, 4468, 4932, 5427, 5954, 6514, 7108, 7737, 8402, 9104, 9844, 10623, 11442, 12302, 13204, 14149, 15138, 16172, 17252, 18379, 19554, 20778

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OFFSET

3,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=3..49.

FORMULA

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

EXAMPLE

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.

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MATHEMATICA

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

CROSSREFS

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

Essentially same as A005581(n)+2.