cp's OEIS Frontend

A121081 Number of partitions of n into parts with at most one 1 and at most one 2.

%I A121081 #10 Jun 02 2018 06:47:46
%S A121081 1,1,2,2,3,5,6,8,11,14,18,24,30,38,49,61,76,96,118,146,181,221,270,
%T A121081 331,401,486,589,709,852,1025,1225,1463,1746,2075,2463,2922,3453,4077,
%U A121081 4808,5656,6644,7798,9130,10678,12475,14547,16942,19714,22898,26570,30798
%N A121081 Number of partitions of n into parts with at most one 1 and at most one 2.
%C A121081 a(n) is also the number of partitions of n with no part equal to 2 or 4. [From _Shanzhen Gao_, Oct 28 2010]
%F A121081 a(n) = A121659(n) + A008483(n-3) for n>2. - _Reinhard Zumkeller_, Aug 14 2006
%F A121081 G.f.: (1+x)*(1+x^2)/Product_{k>=3} (1-x^k). - _Vladeta Jovovic_, Aug 13 2006
%F A121081 a(n) = A000041(n)-A000041(n-2)-A000041(n-4)+A000041(n-6), n>5. - _Vladeta Jovovic_, Aug 13 2006
%F A121081 Given by p(n)-p(n-2)-p(n-4)+p(n-6) where p(n)=A000041(n). - _Shanzhen Gao_, Oct 28 2010
%F A121081 a(n) ~ exp(Pi*sqrt(2*n/3)) * Pi^2 / (3^(3/2) * n^2). - _Vaclav Kotesovec_, Jun 02 2018
%e A121081 a(8)=#{8,7+1,6+2,5+3,5+2+1,4+4,4+3+1,3+3+2}=8;
%e A121081 a(9)=#{9,8+1,7+2,6+3,6+2+1,5+4,5+3+1,4+4+1,4+3+2,3+3+3,3+3+2+1}=11.
%Y A121081 Cf. A027336.
%K A121081 nonn
%O A121081 1,3
%A A121081 _Reinhard Zumkeller_, Aug 11 2006