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 A256857 #36 Feb 16 2025 08:33:25
%S A256857 0,1,8,24,52,95,156,238,344,477,640,836,1068,1339,1652,2010,2416,2873,
%T A256857 3384,3952,4580,5271,6028,6854,7752,8725,9776,10908,12124,13427,14820,
%U A256857 16306,17888,19569,21352,23240,25236,27343,29564,31902,34360,36941,39648,42484,45452,48555
%N A256857 a(n) = n*(n^2 + 3*n - 2)/2.
%C A256857 The sequence is the 5th upper diagonal of the array in A139600.
%H A256857 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolygonalNumber.html">Polygonal Number</a>
%H A256857 <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%H A256857 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A256857 G.f.: x*(1 + 4*x -2*x^2)/(1 - x)^4.
%F A256857 a(n) = A057145(n+6,n). - _R. J. Mathar_, Jul 28 2016
%F A256857 a(n) = Sum_{i=1..n} (n-i-1) mod (n+1). - _Wesley Ivan Hurt_, Sep 15 2017
%F A256857 E.g.f.: exp(x)*x*(2 + 6*x + x^2)/2. - _Stefano Spezia_, Jan 20 2024
%t A256857 Table[n (n^2 + 3 n - 2)/2, {n, 0, 40}]
%o A256857 (Magma) [n*(n^2+3*n-2)/2: n in [0..50]]; // _Vincenzo Librandi_, Apr 14 2015
%o A256857 (PARI) vector(50, n, n--; n*(n^2+3*n-2)/2) \\ _Bruno Berselli_, Apr 15 2015
%Y A256857 Cf. A057145, A139600.
%K A256857 nonn,easy
%O A256857 0,3
%A A256857 _Luciano Ancora_, Apr 11 2015
%E A256857 a(41)-a(45) from _Stefano Spezia_, Jan 20 2024