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A329321 a(n) is the total number of odd parts in all partitions of n into consecutive parts. 1
1, 0, 2, 0, 2, 2, 2, 0, 3, 2, 2, 2, 2, 2, 6, 0, 2, 4, 2, 2, 6, 2, 2, 2, 5, 2, 6, 4, 2, 6, 2, 0, 6, 2, 8, 6, 2, 2, 6, 2, 2, 8, 2, 4, 14, 2, 2, 2, 5, 4, 6, 4, 2, 8, 10, 4, 6, 2, 2, 8, 2, 2, 14, 0, 10, 10, 2, 4, 6, 8, 2, 6, 2, 2, 14, 4, 10, 10, 2, 2, 11, 2, 2, 10, 10, 2, 6, 6, 2, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n) = 0 if and only if n is an even power of 2.

LINKS

Table of n, a(n) for n=1..90.

FORMULA

a(n) = A204217(n) - A329322(n).

EXAMPLE

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 six odd parts, they are [15, 7, 5, 5, 3, 1], so a(15) = 6.

CROSSREFS

Cf. A204217 (total number of parts).

Cf. A000079, A001227, A002131, A237048, A245579, A285898, A285914, A286000, A286001, A299765, A328361, A328365, A329322.

Sequence in context: A102395 A127504 A321665 * A334239 A335062 A047917

Adjacent sequences:  A329318 A329319 A329320 * A329322 A329323 A329324

KEYWORD

nonn

AUTHOR

Omar E. Pol, Nov 10 2019

STATUS

approved

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Last modified May 17 18:29 EDT 2021. Contains 343987 sequences. (Running on oeis4.)