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A263228 a(n) = 2*n*(16*n - 13).

%I A263228 #25 Mar 05 2025 01:12:14
%S A263228 0,6,76,210,408,670,996,1386,1840,2358,2940,3586,4296,5070,5908,6810,
%T A263228 7776,8806,9900,11058,12280,13566,14916,16330,17808,19350,20956,22626,
%U A263228 24360,26158,28020,29946,31936,33990,36108,38290,40536,42846,45220,47658,50160
%N A263228 a(n) = 2*n*(16*n - 13).
%C A263228 For n>=3, a(n) = the Wiener index of the Jahangir graph J_{4,n}. The Jahangir graph J_{4,n} is a connected graph consisting of a cycle graph C(4*n) and one additional center vertex that is adjacent to n vertices of C(4*n) at distances 4 to each other on C(4*n). In the Farahani reference the expression in Theorem 2 is accidentally incorrect; it should be 2*m*(16*m - 13).
%C A263228 The Hosoya polynomial of J_{4,n} is 5*n*x + n*(n+11)*x^2/2 + n*(2*n+1)*x^3 + n*(3*n-4)*x^4 + 2*n*(n-2)*x^5 + n*(n-3)*x^6/2 (see the Farahani reference, p. 234, last line; however, the expression in Theorem 1, p. 233, is accidentally incorrect).
%H A263228 M. R. Farahani, <a href="https://www.researchgate.net/publication/276059305_Hosoya_Polynomial_of_Jahangir_graphs_J4m_101">Hosoya polynomial and of Jahangir graphs J_{4,m}</a>, Global J. Math, 3 (1), 232-236, 2015.
%H A263228 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A263228 G.f.: 2*x*(3+29*x)/(1-x)^3.
%F A263228 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%p A263228 seq(32*n^2 - 26*n, n=0..40);
%t A263228 Table[2 n (16 n - 13), {n, 0, 40}] (* _Bruno Berselli_, Oct 15 2015 *)
%o A263228 (Magma) [2*n*(16*n-13): n in [0..60]]; // _Vincenzo Librandi_, Oct 15 2015
%o A263228 (PARI) vector(50, n, n--; 2*n*(16*n-13)) \\ _Altug Alkan_, Oct 15 2015
%Y A263228 Cf. A049598, A263226, A263227, A263229, A263231.
%K A263228 nonn,easy
%O A263228 0,2
%A A263228 _Emeric Deutsch_, Oct 13 2015