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 A263231 #15 Mar 05 2025 01:12:08
%S A263231 0,-7,11,54,122,215,333,476,644,837,1055,1298,1566,1859,2177,2520,
%T A263231 2888,3281,3699,4142,4610,5103,5621,6164,6732,7325,7943,8586,9254,
%U A263231 9947,10665,11408,12176,12969,13787,14630,15498,16391,17309,18252,19220
%N A263231 a(n) = n*(25*n - 39)/2.
%C A263231 For n>=3, a(n) = the hyper-Wiener index of the Jahangir graph J_{2,n}. The Jahangir graph J_{2,n} is a connected graph consisting of a cycle graph C(2*n) and one additional center vertex that is adjacent to n vertices of C(2*n) at distances 2 to each other on C(2*n).
%C A263231 The Hosoya polynomial of J_{2,n} is 3*n*x + n*(n+3)*x^2/2 + n*(n-2)*x^3 + n*(n-3)*x^4/2.
%D A263231 M. R. Farahani, Hosoya polynomial and Wiener index of Jahangir graphs J_{2,m}, Pacific J. Appl. Math, 7 (3), 2015.
%H A263231 Reinhard Zumkeller, <a href="/A263231/b263231.txt">Table of n, a(n) for n = 0..10000</a>
%H A263231 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A263231 G.f.: x*(32*x-7)/(1-x)^3.
%F A263231 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%p A263231 seq((25*n^2 - 39*n)/2, n=0..40);
%t A263231 Table[n (25 n - 39)/2, {n, 0, 40}]
%o A263231 (PARI) vector(50, n, n--; n*(25*n-39)/2)
%o A263231 (PARI) concat(0, Vec(x*(32*x-7)/(1-x)^3 + O(x^100))) \\ _Altug Alkan_, Oct 18 2015
%o A263231 (Haskell)
%o A263231 a263231 n = n * (25 * n - 39) `div` 2
%o A263231 a263231_list = 0 : -7 : 11 : zipWith (+) a263231_list
%o A263231 (map (* 3) $ tail $ zipWith (-) (tail a263231_list) a263231_list)
%o A263231 -- _Reinhard Zumkeller_, Nov 04 2015
%Y A263231 Cf. A263226, A263227, A263228, A263229, A263230.
%K A263231 sign,easy
%O A263231 0,2
%A A263231 _Emeric Deutsch_, Oct 14 2015