A196025 Total sum of parts greater than 1 in all the partitions of n except one copy of the smallest part greater than 1 of every partition.

0, 0, 0, 2, 5, 16, 30, 63, 108, 189, 298, 483, 720, 1092, 1582, 2297, 3225, 4551, 6244, 8592, 11590, 15622, 20741, 27536, 36066, 47198, 61150, 79077, 101391, 129808, 164934, 209213, 263745, 331807, 415229, 518656, 644719, 799926, 988432, 1218979

Offset: 1

Author

Omar E. Pol, Oct 27 2011

Keywords

• nonn

Comments

Also partial sums of A182709. Total sum of emergent parts in all partitions of all numbers <= n.

Also total sum 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

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A026905, A046746, A066186, A135010, A138121, A182699, A182707, A182709, A183152, A193827, A196039, A196930, A196931, A198381.

Formula

a(n) = A066186(n) - A196039(n).

a(n) ~ exp(Pi*sqrt(2*n/3)) / (4*sqrt(3)). - Vaclav Kotesovec, Jul 06 2019