A145067 - OEIS

%I #18 May 09 2024 13:25:38

%S 0,-1,1,8,22,45,79,126,188,267,365,484,626,793,987,1210,1464,1751,

%T 2073,2432,2830,3269,3751,4278,4852,5475,6149,6876,7658,8497,9395,

%U 10354,11376,12463,13617,14840,16134,17501,18943,20462,22060,23739,25501

%N Zero followed by partial sums of A008865.

%F a(1) = 0; a(n) = a(n-1) + (n-1)^2 - 2 for n > 0.

%F 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 G.f.: -x^2*(1-5*x+2*x^2)/(1-x)^4. - _Colin Barker_, Apr 04 2012

%e a(2) = a(1) + 1^2 - 2 = 0 + 1 - 2 = -1; a(3) = a(2) + 2^2 - 2 = -1 + 4 - 2 = 1.

%t lst={0}; s=0; Do[s+=n^2 - 2; AppendTo[lst, s], {n, 5!}]; lst

%t Table[Sum[(i^2 + n - 1), {i, 0, n}], {n, -1, 41}] (* _Zerinvary Lajos_, Jul 11 2009 *)

%t Join[{0},Accumulate[Range[50]^2-2]] (* _Harvey P. Dale_, Jul 23 2018 *)

%o (PARI) {a=2; for(n=0, 42, print1(a=a+n^2-2, ","))}

%Y 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 sign,easy

%O 1,4

%A _Vladimir Joseph Stephan Orlovsky_, Sep 30 2008

%E Edited by _Klaus Brockhaus_, Oct 17 2008