A027337 - OEIS

%I #15 Nov 04 2016 12:04:40

%S 1,1,2,2,4,5,8,10,15,19,27,34,47,59,79,99,130,162,209,259,330,407,512,

%T 628,783,956,1181,1435,1760,2129,2594,3124,3784,4539,5468,6534,7834,

%U 9327,11132,13208,15701,18568,21989,25923,30592,35960,42297,49579,58139,67967

%N Number of partitions of n that do not contain 3 as a part.

%C a(n) is also the number of partitions of n with less than three 1's. - _Geoffrey Critzer_, Jun 20 2014

%F G.f.: (1-x^3) Product_{m>0} 1/(1-x^m).

%F a(n) = A000041(n) - A000041(n-3).

%F a(n) ~ Pi * exp(sqrt(2*n/3)*Pi) / (4*sqrt(2)*n^(3/2)) * (1 - (3*sqrt(3/2)/Pi + Pi/(24*sqrt(6)) + 3*Pi/(2*sqrt(6)))/sqrt(n) + (37/8 + 9/(2*Pi^2) + 1801*Pi^2/6912)/n). - _Vaclav Kotesovec_, Nov 04 2016

%t nn=49;CoefficientList[Series[(1-x^3)Product[1/(1-x^i),{i,1,nn}],{x,0,nn}],x] (* _Geoffrey Critzer_, Jun 20 2014 *)

%o (PARI) a(n)=if(n<0,0,polcoeff((1-x^3)/eta(x+x*O(x^n)),n))

%Y Cf. A000041, A027336, A027338.

%Y Column k=0 of A263232.

%Y Column 3 of A175788.

%K nonn

%O 0,3

%A _Clark Kimberling_