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 A101357 #36 Feb 16 2025 08:32:55
%S A101357 0,1,3,9,25,60,126,238,414,675,1045,1551,2223,3094,4200,5580,7276,
%T A101357 9333,11799,14725,18165,22176,26818,32154,38250,45175,53001,61803,
%U A101357 71659,82650,94860,108376,123288,139689,157675,177345,198801,222148,247494
%N A101357 Partial sums of A060354.
%C A101357 The Ca4 triangle sums of A139600 are given by the terms of this sequence. For the definitions of the Ca4 and other triangle sums see A180662. - _Johannes W. Meijer_, Apr 29 2011
%H A101357 Vincenzo Librandi, <a href="/A101357/b101357.txt">Table of n, a(n) for n = 0..10000</a>
%H A101357 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolygonalNumber.html">Polygonal number</a>
%H A101357 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A101357 a(n) = Sum_{i=0..n} (i(i-2)^2 + i^2)/2.
%F A101357 a(n) = A004255(n), n > 0. - _R. J. Mathar_, Sep 02 2008
%F A101357 a(n) = binomial(n+3,4) - 2*binomial(n+2,4) + 4*binomial(n+1,4).
%F A101357 a(n) = (n^4 - 2*n^3 + 3*n^2 + 6*n)/8. - _Johannes W. Meijer_, Apr 29 2011
%F A101357 G.f.: -x*(4*x^2 - 2*x + 1) / (x-1)^5. - _Colin Barker_, Apr 29 2013
%t A101357 Table[Sum[(i*(i - 2)^2 + i^2)/2, {i, 0, n}], {n, 0, 38}]
%t A101357 Accumulate[Table[(n (n-2)^2+n^2)/2,{n,0,50}]] (* _Harvey P. Dale_, Aug 05 2011 *)
%o A101357 (Magma) [(n^4-2*n^3+3*n^2+6*n)/8: n in [0..40]]; // _Vincenzo Librandi_, Aug 06 2011
%o A101357 (PARI) a(n)=(n^4-2*n^3+3*n^2+6*n)/8 \\ _Charles R Greathouse IV_, Oct 16 2015
%Y A101357 Cf. A060354, A000332.
%K A101357 easy,nonn
%O A101357 0,3
%A A101357 _Jonathan Vos Post_, Dec 25 2004
%E A101357 More terms from _Joshua Zucker_, May 12 2006
%E A101357 Edited by _Stefan Steinerberger_, Aug 01 2007