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 A159920 #54 Jul 19 2025 00:17:45
%S A159920 4,14,32,60,100,154,224,312,420,550,704,884,1092,1330,1600,1904,2244,
%T A159920 2622,3040,3500,4004,4554,5152,5800,6500,7254,8064,8932,9860,10850,
%U A159920 11904,13024,14212,15470,16800,18204,19684,21242,22880,24600,26404
%N A159920 Sums of the antidiagonals of Sundaram's sieve (A159919).
%C A159920 For every n >= 2, a(n) is the sum of numbers in the (n-1)-th antidiagonal of the Sundaram sieve. (It is not clear why the offset was set to 2 rather than 1.) Thus, if T(j, k) is the element in row j and column k of the Sundaram sieve, we have a(n) = Sum_{i = 1..n-1} T(i, n-i) = Sum_{i = 1..n-1} (2*i*(n-i) + i + (n-i)) = (n - 1)*n*(n + 4)/3 for the sum of the numbers in the (n-1)-th antidiagonal. - _Petros Hadjicostas_, Jun 19 2019
%H A159920 G. C. Greubel, <a href="/A159920/b159920.txt">Table of n, a(n) for n = 2..1000</a>
%H A159920 Andrew Baxter, <a href="http://banach.millersville.edu/~bob/math478/History/Sundaram.html">Sundaram's Sieve</a>.
%H A159920 Julian Havil, <a href="http://plus.maths.org/issue50/features/havil/index.html">Sundaram's Sieve</a>, Plus Magazine, March 2009.
%H A159920 New Zealand Maths, <a href="https://web.archive.org/web/20040309001101/www.nzmaths.co.nz/HelpCentre/Newsletter18.pdf">Newletter 18</a>, October 2002.
%H A159920 Wikipedia, <a href="http://en.wikipedia.org/wiki/Sieve_of_Sundaram">Sundaram's Sieve</a>.
%H A159920 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A159920 a(n) = (n - 1)*n*(n + 4)/3.
%F A159920 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
%F A159920 a(n) = 2*A005581(n), n > 1.
%F A159920 a(n) = Sum_{i=1..n-1} i*(i + 3). - _Wesley Ivan Hurt_, Oct 19 2013
%F A159920 From _G. C. Greubel_, Oct 03 2022: (Start)
%F A159920 G.f.: 2*x^2*(2 - x)/(1-x)^4.
%F A159920 E.g.f.: (1/3)*x^2*(6 + x)*exp(x). (End)
%F A159920 a(n) = 2*A097900(n)/(n-2)! for n >= 2. - _Cullen M. Vaney_, Jul 14 2025
%e A159920 For n = 5, (4*5*9)/3 = 60. Indeed, T(1, 4) + T(2, 3) + T(3, 2) + T(4, 1) = 13 + 17 + 17 + 13 = 60 for the sum of the terms in the 4th antidiagonal of the Sundaram sieve.
%p A159920 A159920:=n->n*(n-1)*(n+4)/3; seq(A159920(k), k=2..100); # _Wesley Ivan Hurt_, Oct 19 2013
%t A159920 Table[(n-1)*n*(n+4)/3,{n,2,60}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 28 2010 *)
%t A159920 LinearRecurrence[{4,-6,4,-1},{4,14,32,60},61] (* _Harvey P. Dale_, Apr 23 2011 *)
%o A159920 (Magma) [n*(n-1)*(n+4)/3: n in [2..60]]; // _G. C. Greubel_, Oct 03 2022
%o A159920 (SageMath) [n*(n-1)*(n+4)/3 for n in range(2,60)] # _G. C. Greubel_, Oct 03 2022
%Y A159920 Cf. A005581, A097900, A159919.
%K A159920 nonn,easy
%O A159920 2,1
%A A159920 _Russell Walsmith_, Apr 26 2009