A198381 Total number of parts greater than 1 in all partitions of n minus the number of partitions of n into parts each less than n.

0, 0, 0, 0, 1, 2, 6, 10, 20, 32, 54, 81, 128, 184, 273, 385, 549, 754, 1048, 1412, 1917, 2547, 3392, 4444, 5837, 7556, 9791, 12553, 16086, 20429, 25935, 32665, 41108, 51404, 64190, 79721, 98882, 122043, 150417, 184618, 226239

Offset

0,6

Comments

Also partial sums of A182699. Total number of emergent parts in all partitions of the numbers <= n.

Also total number of parts of all regions of n that do not contain 1 as a part (Cf. A083751, A187219). - Omar E. Pol, Mar 04 2012

Links

Table of n, a(n) for n=0..40.

Formula

a(n) = A096541(n) - A000065(n) = 1 + A096541(n) - A000041(n) = 1 + A006128(n) - A000070(n).

a(n) = A006128(n) - A026905(n), n >= 1.

Crossrefs

Cf. A000041, A000065, A000070, A006128, A026905, A093694, A096541, A135010, A138121, A182699, A182707, A182709, A183152, A193827, A196930, A196931.

Sequence in context: A168152 A211982 A096338 * A309846 A309874 A317759

Adjacent sequences: A198378 A198379 A198380 * A198382 A198383 A198384

Keyword

nonn

Author

Omar E. Pol, Oct 27 2011

Status

approved