A145066 Partial sums of A002522, starting at n=1.

2, 7, 17, 34, 60, 97, 147, 212, 294, 395, 517, 662, 832, 1029, 1255, 1512, 1802, 2127, 2489, 2890, 3332, 3817, 4347, 4924, 5550, 6227, 6957, 7742, 8584, 9485, 10447, 11472, 12562, 13719, 14945, 16242, 17612, 19057, 20579, 22180, 23862, 25627

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Sep 30 2008

Keywords

• nonn
• easy

Examples

			a(2) = a(1) + 2^2 + 1 = 2 + 4 + 1 = 7; a(3) = a(2) + 3^2 + 1 = 7 + 9 + 1 = 17.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A002522 (n^2 + 1), A005563 ((n+1)^2 - 1), A051925 (zero followed by partial sums of A005563), A081489 (partial sums of A002522 starting at n=0).

Programs

Mathematica

Accumulate[Range[50]^2+1] (* Harvey P. Dale, Dec 07 2016 *)

PARI

{a=0; for(n=1, 42, print1(a=a+n^2+1, ","))}

Python

def A145066(n): return (n*(n*(2*n + 3) + 1))//6 + n # Chai Wah Wu, Oct 30 2024

Formula

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

From Christoph Pacher (christoph.pacher(AT)ait.ac.at), Jul 23 2010: (Start)

a(n) = Sum_{k=1..n} (k^2 + 1).

a(n) = A000330(n) + n.

a(n) = n*(n+1)*(2*n+1)/6 + n. (End)

G.f.: x*(2-x+x^2)/(1-x)^4. - Colin Barker, Apr 04 2012

E.g.f.: (1/6)*x*(12 + 9*x + 2*x^2)*exp(x). - G. C. Greubel, Jul 22 2017

a(n) = A081489(n+1) - 1. - Jianing Song, Oct 10 2021

Extensions

Edited by Klaus Brockhaus, Oct 17 2008