cp's OEIS Frontend

A145067 Zero followed by partial sums of A008865.

%I A145067 #18 May 09 2024 13:25:38
%S A145067 0,-1,1,8,22,45,79,126,188,267,365,484,626,793,987,1210,1464,1751,
%T A145067 2073,2432,2830,3269,3751,4278,4852,5475,6149,6876,7658,8497,9395,
%U A145067 10354,11376,12463,13617,14840,16134,17501,18943,20462,22060,23739,25501
%N A145067 Zero followed by partial sums of A008865.
%F A145067 a(1) = 0; a(n) = a(n-1) + (n-1)^2 - 2 for n > 0.
%F A145067 a(n) = Sum_{k=1...n-1} (k^2-2) = A000330(n-1)-2*A000027(n-1) = (n-1)*(2*n^2-n-12)/6. - Christoph Pacher (christoph.pacher(AT)ait.ac.at), Jul 23 2010
%F A145067 G.f.: -x^2*(1-5*x+2*x^2)/(1-x)^4. - _Colin Barker_, Apr 04 2012
%e A145067 a(2) = a(1) + 1^2 - 2 = 0 + 1 - 2 = -1; a(3) = a(2) + 2^2 - 2 = -1 + 4 - 2 = 1.
%t A145067 lst={0}; s=0; Do[s+=n^2 - 2; AppendTo[lst, s], {n, 5!}]; lst
%t A145067 Table[Sum[(i^2 + n - 1), {i, 0, n}], {n, -1, 41}] (* _Zerinvary Lajos_, Jul 11 2009 *)
%t A145067 Join[{0},Accumulate[Range[50]^2-2]] (* _Harvey P. Dale_, Jul 23 2018 *)
%o A145067 (PARI) {a=2; for(n=0, 42, print1(a=a+n^2-2, ","))}
%Y A145067 Cf. A008865 (n^2 - 2), A002522 (n^2 + 1), A145066 (partial sums of A002522, starting at n=1), A005563 ((n+1)^2 - 1), A051925 (zero followed by partial sums of A005563), A000330.
%K A145067 sign,easy
%O A145067 1,4
%A A145067 _Vladimir Joseph Stephan Orlovsky_, Sep 30 2008
%E A145067 Edited by _Klaus Brockhaus_, Oct 17 2008