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

1,3

Comments

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

Links

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

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

Example

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.

Crossrefs

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

Sequence in context: A008104 A227358 A008252 * A022495 A238489 A002537

Adjacent sequences: A182704 A182705 A182706 * A182708 A182709 A182710

Keyword

nonn,easy

Author

Omar E. Pol, Nov 28 2010

Status

approved