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%I #38 Sep 07 2019 20:06:13
%S -1,0,0,0,0,1,1,3,4,7,10,16,21,32,43,60,80,110,143,192,248,325,417,
%T 539,682,872,1097,1384,1728,2163,2679,3327,4097,5048,6182,7570,9216,
%U 11223,13599,16467,19862,23940,28747,34496,41260,49302,58751,69938,83039,98502,116572
%N Number of partitions of n that contain {1,2} minus number of partitions of n that contain neither 1 nor 2.
%C a(n) > 0 for all n >= 5.
%F a(n) = A000041(n-2) + A000041(n-1) - A000041(n).
%F a(n) ~ exp(Pi*sqrt(2*n/3)) / (4*n*sqrt(3)) * (1 - (sqrt(3/2)/Pi + 73*Pi/(24*sqrt(6)))/sqrt(n) + (73/16 + 3025*Pi^2/6912)/n). - _Vaclav Kotesovec_, Sep 03 2019
%F G.f.: (q^2+q-1)/Product_{n>=1} (1-q^n). - _Shouvik Datta_, Sep 07 2019
%t Table[-(PartitionsP[n] - PartitionsP[n - 1] - PartitionsP[n - 2]), {n, 0, 20}] (* _Shouvik Datta_, Sep 07 2019 *)
%o (PARI) a(n) = numbpart(n-2) + numbpart(n-1) - numbpart(n); \\ _Michel Marcus_, Sep 03 2019
%Y Cf. A000041.
%K easy,sign
%O 0,8
%A _Max Alekseyev_, Sep 03 2019
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