A285899 Total number of parts in all partitions of all positive integers <= n into consecutive parts.

1, 2, 5, 6, 9, 13, 16, 17, 23, 28, 31, 35, 38, 43, 54, 55, 58, 66, 69, 75, 87, 92, 95, 99, 107, 112, 124, 132, 135, 148, 151, 152, 164, 169, 184, 196, 199, 204, 216, 222, 225, 240, 243, 252, 278, 283, 286, 290, 300, 310, 322, 331, 334, 351, 369, 377, 389, 394, 397, 414, 417, 422, 450, 451, 469, 488, 491, 500, 512, 529

Offset

1,2

Comments

Partial sums of A204217.

Sum of first n rows of the triangle A285914.

Where records occur in A328365. - Omar E. Pol, Oct 22 2019

Row sums of A328368. - Omar E. Pol, Nov 04 2019

Links

Table of n, a(n) for n=1..70.

Example

For n = 15 there are four partitions of 15 into consecutive parts: [15], [8, 7], [6, 5, 4] and [5, 4, 3, 2, 1]. The total number of parts in these four partitions is 11, and a(14) = 43, so a(15) = 43 + 11 = 54.

Crossrefs

Cf. A001227, A196020, A204217, A235791, A237048, A237591, A237593, A245092, A285900, A285914, A299765, A328361, A328362, A328365, A328368.

Sequence in context: A286003 A094350 A104857 * A055198 A103982 A030488

Adjacent sequences: A285896 A285897 A285898 * A285900 A285901 A285902

Keyword

nonn

Author

Omar E. Pol, May 02 2017

Status

approved