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

%I A349416 #33 Dec 18 2021 23:42:50
%S A349416 25,54,100,167,259,380,534,725,957,1234,1560,1939,2375,2872,3434,4065,
%T A349416 4769,5550,6412,7359,8395,9524,10750,12077,13509,15050,16704,18475,
%U A349416 20367,22384,24530,26809,29225,31782,34484,37335,40339,43500,46822,50309,53965,57794,61800,65987
%N A349416 a(n) is the Wiener index of a broom on 2n vertices of which n+2 are pendant.
%C A349416 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.
%H A349416 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A349416 a(n) = 2n^3/3 + n^2/2 + 5n/6.
%e A349416 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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%t A349416 nterms=50;Table[2n^3/3+n^2/2+5n/6,{n,3,nterms+2}] (* _Paolo Xausa_, Nov 22 2021 *)
%Y A349416 Cf. A349417 (sling), A349418 (tridon).
%K A349416 nonn,easy
%O A349416 3,1
%A A349416 _Julian Allagan_, Nov 16 2021