A329322 a(n) is the total number of even parts in all partitions of n into consecutive parts.

0, 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 2, 1, 3, 5, 1, 1, 4, 1, 4, 6, 3, 1, 2, 3, 3, 6, 4, 1, 7, 1, 1, 6, 3, 7, 6, 1, 3, 6, 4, 1, 7, 1, 5, 12, 3, 1, 2, 5, 6, 6, 5, 1, 9, 8, 4, 6, 3, 1, 9, 1, 3, 14, 1, 8, 9, 1, 5, 6, 9, 1, 7, 1, 3, 13, 5, 11, 10, 1, 4, 10, 3, 1, 9, 8, 3, 6, 6, 1, 18

Offset: 1

Author

Omar E. Pol, Nov 10 2019

Keywords

• nonn

Examples

			For n = 15 there are four partitions of 15 into consecutive part, they are [15], [8, 7], [6, 5, 4], [5, 4, 3, 2, 1]. In total there are five even parts, they are [8, 6, 4, 4, 2], so a(15) = 5.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A204217 (total number of parts).

Cf. A001227, A237048, A245579, A285898, A285914, A286000, A286001, A299765, A328361, A328365, A329321.

Programs

PARI

A329322(n) = { my(i=2, t=!(n%2)); n--; while(n>0, if(!(n%i), t += (!((n/i)%2)+i)\2); n-=i; i++); t }; \\ (After David A. Corneth's program for A204217) - Antti Karttunen, Dec 09 2021

Formula

a(n) = A204217(n) - A329321(n).