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 A227970 #21 Aug 20 2025 10:46:40
%S A227970 0,0,1,6,28,66,153,276,496,780,1225,1770,2556,3486,4753,6216,8128,
%T A227970 10296,13041,16110,19900,24090,29161,34716,41328,48516,56953,66066,
%U A227970 76636,87990,101025,114960,130816,147696,166753,186966,209628,233586,260281,288420,319600,352380,388521,426426
%N A227970 Triangular arithmetic on half-squares: b(n)*(b(n) - 1)/2 where b(n) = floor(n^2/2).
%C A227970 Analogous to A083374 for the squares A000290.
%C A227970 A "mirrored" repeating pattern of cycle length 20 exists in the last digit.
%H A227970 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-6,0,6,-2,-2,1).
%F A227970 Let b(n) = floor(n^2/2), for n => 0, then a(n) = b(n)*(b(n)- 1)/2.
%F A227970 G.f.: -x^2*(1+4*x+14*x^2+4*x^3+x^4) / ( (1+x)^3*(x-1)^5 ). - _R. J. Mathar_, Aug 14 2013
%F A227970 a(n) = binomial(floor(n^2/2), 2). - _Wesley Ivan Hurt_, Sep 27 2013
%p A227970 A227970:=n->binomial(floor(n^2/2),2); seq(A227970(k),k=0..50); # _Wesley Ivan Hurt_, Oct 05 2013
%t A227970 Table[Binomial[Floor[n^2/2], 2], {n, 0, 50}] (* _Wesley Ivan Hurt_, Sep 27 2013 *)
%Y A227970 Cf. A007590, A083374.
%K A227970 nonn,easy,changed
%O A227970 0,4
%A A227970 _Richard R. Forberg_, Aug 01 2013