cp's OEIS Frontend

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.

A263226 a(n) = 15*n^2 - 13*n.

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%I A263226 #23 Sep 08 2022 08:46:14
%S A263226 0,2,34,96,188,310,462,644,856,1098,1370,1672,2004,2366,2758,3180,
%T A263226 3632,4114,4626,5168,5740,6342,6974,7636,8328,9050,9802,10584,11396,
%U A263226 12238,13110,14012,14944,15906,16898,17920,18972,20054,21166,22308,23480,24682,25914
%N A263226 a(n) = 15*n^2 - 13*n.
%C A263226 For n>=3, a(n) = the 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 A263226 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 A263226 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 A263226 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A263226 G.f.: 2*x*(1 + 14*x)/(1 - x)^3. - _Vincenzo Librandi_, Oct 13 2015
%F A263226 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Oct 13 2015
%p A263226 seq(15*n^2-13*n, n = 0 .. 40);
%t A263226 Table[15 n^2 - 13 n, {n, 0, 40}] (* _Vincenzo Librandi_, Oct 13 2015 *)
%t A263226 LinearRecurrence[{3,-3,1},{0,2,34},50] (* _Harvey P. Dale_, Jul 27 2018 *)
%o A263226 (PARI) vector(50, n, n--; 15*n^2 - 13*n) \\ _Altug Alkan_, Oct 12 2015
%o A263226 (Magma) [15*n^2-13*n: n in [0..50]]; // _Bruno Berselli_, Oct 15 2015
%Y A263226 Cf. A049598, A263227, A263228, A263229, A263231.
%K A263226 nonn,easy
%O A263226 0,2
%A A263226 _Emeric Deutsch_, Oct 12 2015