cp's OEIS Frontend

A172033 Number of partitions of n into distinct parts that are 1 or even, i.e., into distinct terms of A004277.

%I A172033 #11 Oct 12 2024 02:00:46
%S A172033 1,1,1,1,1,1,2,2,2,2,3,3,4,4,5,5,6,6,8,8,10,10,12,12,15,15,18,18,22,
%T A172033 22,27,27,32,32,38,38,46,46,54,54,64,64,76,76,89,89,104,104,122,122,
%U A172033 142,142,165,165,192,192,222,222,256,256,296,296,340,340,390,390,448,448
%N A172033 Number of partitions of n into distinct parts that are 1 or even, i.e., into distinct terms of A004277.
%C A172033 A000009 repeated: a(n) = A000009(floor(n/2)).
%F A172033 G.f.: (1+q) * Product_{n>=1} (1 + q^(2*n)). - _Joerg Arndt_, Mar 11 2014
%e A172033 a(12) = #{12, 10+2, 8+4, 6+4+2} = 4;
%e A172033 a(13) = #{12+1, 10+2+1, 8+4+1, 6+4+2+1} = 4;
%e A172033 a(14) = #{14, 12+2, 10+4, 8+6, 8+4+2} = 5.
%o A172033 (PARI) my(N=68, q='q+O('q^N)); Vec( (1+q)*prod(n=1,N,1+q^(2*n)) ) \\ _Joerg Arndt_, Mar 11 2014
%Y A172033 Cf. A025065.
%K A172033 nonn
%O A172033 0,7
%A A172033 _Reinhard Zumkeller_, Jan 23 2010