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A182707
Sum of the parts of all partitions of n-1 plus the sum of the emergent parts of the partitions of n.
6
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.
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Nov 28 2010
STATUS
approved