This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A263227 #25 Nov 16 2024 06:31:19
%S A263227 0,-11,45,168,358,615,939,1330,1788,2313,2905,3564,4290,5083,5943,
%T A263227 6870,7864,8925,10053,11248,12510,13839,15235,16698,18228,19825,21489,
%U A263227 23220,25018,26883,28815,30814,32880,35013,37213,39480,41814,44215,46683,49218,51820
%N A263227 a(n) = n*(67*n - 89)/2.
%C A263227 For n>=3, a(n) = the hyper-Wiener index of the Jahangir graph J_{3,n}. The Jahangir graph J_{3,n} is a connected graph consisting of a cycle graph C(3n) and one additional center vertex that is adjacent to n vertices of C(3n) at distances 3 to each other on C(3n).
%C A263227 The Hosoya polynomial of J_(3,n) is 4nx + (1/2)n(n+9)x^2 + 2n(n-1)x^3 + n(2n-5)x^4.
%H A263227 M. R. Farahani, <a href="http://frdint.com/the_wiener_index_and.pdf">The Wiener index and Hosoya polynomial of a class of Jahangir graphs J_{3,m}</a>, Fundamental J. Math. and Math. Sci., 3 (1), 91-96, 2015.
%H A263227 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A263227 G.f.: x*(-11+78*x)/(1-x)^3. - _Vincenzo Librandi_, Oct 13 2015
%F A263227 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Oct 13 2015
%p A263227 seq((1/2)*n*(67*n-89), n = 0 .. 40);
%t A263227 Table[n (67 n - 89)/2, {n, 0, 40}] (* _Vincenzo Librandi_, Oct 13 2015 *)
%o A263227 (PARI) vector(50, n, n--; n*(67*n-89)/2) \\ _Altug Alkan_, Oct 12 2015
%o A263227 (Magma) [n*(67*n-89)/2: n in [0..40]]; // _Bruno Berselli_, Oct 15 2015
%Y A263227 Cf. A049598, A263226, A263228, A263229, A263231.
%K A263227 sign,easy
%O A263227 0,2
%A A263227 _Emeric Deutsch_, Oct 12 2015