A182707 - OEIS

%I #26 Sep 02 2020 19:02:37

%S 0,1,4,11,23,46,80,138,221,351,529,801,1161,1685,2380,3355,4624,6375,

%T 8623,11658,15538,20664,27163,35660,46330,60082,77288,99197,126418,

%U 160802,203246,256381,321700,402781,501962,624332,773235,955776,1177076,1446762,1772308

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

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

%H Vaclav Kotesovec, <a href="/A182707/b182707.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Jason Kimberley)

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

%F 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

%e 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.

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

%K nonn,easy

%O 1,3

%A _Omar E. Pol_, Nov 28 2010