A071754 a(n) = Sum_{k=0..n} pp(k) where pp(k) is the parity of p(k) the k-th partition number = A040051(k).

1, 2, 2, 3, 4, 5, 6, 7, 7, 7, 7, 7, 8, 9, 10, 10, 11, 12, 13, 13, 14, 14, 14, 15, 16, 16, 16, 16, 16, 17, 17, 17, 18, 19, 19, 20, 21, 22, 23, 24, 24, 25, 25, 26, 27, 27, 27, 27, 28, 29, 29, 30, 31, 32, 33, 33, 34, 34, 34, 34, 35, 36, 36, 37, 37, 37, 37, 38, 39, 40, 40, 41, 42, 43

Offset: 0

Author

Benoit Cloitre, Jun 24 2002

Keywords

• easy
• nonn

Comments

It appears that there is a constant A > 0 such that for any n>1: An/log(n) < 2a(n) - n < n/Log(n) and that lim n ->infinity (2*a(n) - n )/(n/Log(n)) exists. - Benoit Cloitre, Jan 29 2006

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A040051.

Programs

Mathematica

Table[ Mod[ PartitionsP[n], 2], {n, 0, 73}] // Accumulate (* Jean-François Alcover, Jun 18 2013 *)

PARI

\ps100 s=0; for(n=0,80,s=s+(1-(-1)^polcoeff(1/eta(x),n,x))/2; print1(s,", "))

PARI

a(n) = sum(k=0, n, numbpart(k) % 2); \\ Michel Marcus, Feb 24 2023