A145068 Zero followed by partial sums of A059100, starting at n=1.

0, 3, 9, 20, 38, 65, 103, 154, 220, 303, 405, 528, 674, 845, 1043, 1270, 1528, 1819, 2145, 2508, 2910, 3353, 3839, 4370, 4948, 5575, 6253, 6984, 7770, 8613, 9515, 10478, 11504, 12595, 13753, 14980, 16278, 17649, 19095, 20618, 22220, 23903, 25669

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Sep 30 2008

Keywords

• nonn
• easy

Examples

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

Crossrefs

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).

Programs

Mathematica

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

PARI

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

Formula

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

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

Extensions

Edited by Klaus Brockhaus, Oct 21 2008