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%I #8 Jul 20 2017 01:49:23
%S 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 22,27,27,32,32,38,38,46,46,54,54,64,64,76,76,89,89,104,104,122,122,
%U 142,142,165,165,192,192,222,222,256,256,296,296,340,340,390,390,448,448
%N Number of partitions of n into distinct parts that are 1 or even, i.e., into distinct terms of A004277.
%C A000009 repeated: a(n) = A000009(floor(n/2)).
%F G.f.: (1+q) * Product_{n>=1})(1 + q^(2*n)). [_Joerg Arndt_, Mar 11 2014]
%e a(12) = #{12, 10+2, 8+4, 6+4+2} = 4;
%e a(13) = #{12+1, 10+2+1, 8+4+1, 6+4+2+1} = 4;
%e a(14) = #{14, 12+2, 10+4, 8+6, 8+4+2} = 5.
%o (PARI) N=66; q='q+O('q^N); Vec( (1+q)*prod(n=1,N,1+q^(2*n)) ) \\ _Joerg Arndt_, Mar 11 2014
%Y Cf. A025065.
%K nonn
%O 0,7
%A _Reinhard Zumkeller_, Jan 23 2010
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