A145068 - OEIS

%I #5 Jan 13 2015 09:32:03

%S 0,3,9,20,38,65,103,154,220,303,405,528,674,845,1043,1270,1528,1819,

%T 2145,2508,2910,3353,3839,4370,4948,5575,6253,6984,7770,8613,9515,

%U 10478,11504,12595,13753,14980,16278,17649,19095,20618,22220,23903,25669

%N Zero followed by partial sums of A059100, starting at n=1.

%F G.f.: x*(3-3*x+2*x^2)/(1-x)^4.

%F a(1) = 0; a(n) = sum_{j=1..n-1} A059100(j) = a(n-1) + (n-1)^2 + 2 for n > 1.

%e a(2) = a(1) + 1^2 + 2 = 0 + 1 + 2 = 3; a(3) = a(2) + 2^2 + 2 = 3 + 4 + 2 = 9.

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

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

%Y Cf. A059100 (n^2+2), A002522 (n^2 + 1), A145066 (partial sums of A002522, starting at n=1), A008865 (n^2 - 2), A145067 (zero followed by partial sums of A008865), A005563 ((n+1)^2 - 1), A051925 (zero followed by partial sums of A005563).

%K nonn,easy

%O 1,2

%A _Vladimir Joseph Stephan Orlovsky_, Sep 30 2008

%E Edited by _Klaus Brockhaus_, Oct 21 2008