A182707 Sum of the parts of all partitions of n-1 plus the sum of the emergent parts of the partitions of n.

0, 1, 4, 11, 23, 46, 80, 138, 221, 351, 529, 801, 1161, 1685, 2380, 3355, 4624, 6375, 8623, 11658, 15538, 20664, 27163, 35660, 46330, 60082, 77288, 99197, 126418, 160802, 203246, 256381, 321700, 402781, 501962, 624332, 773235, 955776, 1177076, 1446762, 1772308

Offset: 1

Author

Omar E. Pol, Nov 28 2010

Keywords

• nonn
• easy

Comments

For more information about the emergent parts of the partitions of n see A182699 and A182709.

Examples

			For n = 6 the partitions of 6-1=5 are (5);(3+2);(4+1);(2+2+1);(3+1+1);(2+1+1+1);(1+1+1+1+1) and the sum of the parts give 35, the same as 5*7. By other hand the emergent parts of the partitions of 6 are (2+2);(4);(3) and the sum give 11, so a(6) = 35+11 = 46.
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Jason Kimberley)

Crossrefs

Cf. A000041, A046746, A066186, A135010, A138121, A182699, A182708, A182709.

Formula

a(n) = A066186(n) - A046746(n) = A066186(n-1) + A182709(n).

a(n) ~ exp(Pi*sqrt(2*n/3)) / (4*sqrt(3)) * (1 - (sqrt(3/2)/Pi + Pi/(24*sqrt(6)))/sqrt(n)). - Vaclav Kotesovec, Jan 03 2019, extended Jul 06 2019