cp's OEIS Frontend

A129889 Write down n, then n*(n+1).

%I A129889 #24 Sep 03 2025 00:51:37
%S A129889 0,0,1,2,2,6,3,12,4,20,5,30,6,42,7,56,8,72,9,90,10,110,11,132,12,156,
%T A129889 13,182,14,210,15,240,16,272,17,306,18,342,19,380,20,420,21,462,22,
%U A129889 506,23,552,24,600,25,650,26,702,27,756,28,812,29,870,30,930,31,992,32,1056,33
%N A129889 Write down n, then n*(n+1).
%H A129889 Bruno Berselli, <a href="/A129889/b129889.txt">Table of n, a(n) for n = 0..1000</a>
%H A129889 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1).
%F A129889 From _Bruno Berselli_, May 06 2011: (Start)
%F A129889 G.f.: x^2*(1+2*x-x^2)/(1-x^2)^3.
%F A129889 a(n) = ((1+2*n-n^2)*(-1)^n -(1-2*n-n^2))/8.
%F A129889 a(n) = a(n-2) + A124625(n) for n>1. (End)
%p A129889 f:=n-> if n mod 2 = 0 then n/2 else (n^2-1)/4; fi;
%t A129889 Flatten[Table[{n,n(n+1)},{n,0,40}]] (* _Harvey P. Dale_, Jun 21 2015 *)
%o A129889 (Magma) [IsEven(n) select n/2 else (n^2-1)/4: n in [0..66]]; // _Bruno Berselli_, May 06 2011
%Y A129889 Cf. A124625.
%K A129889 nonn,easy,changed
%O A129889 0,4
%A A129889 _N. J. A. Sloane_, May 26 2007