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%I #16 Sep 08 2019 14:44:08
%S 1,1,1,1,1,1,1,2,2,2,2,3,3,4,5,5,5,5,6,7,8,10,11,11,12,14,16,17,19,20,
%T 21,23,27,30,32,36,38,41,45,50,54,58,64,68,74,80,88,95,102,111,119,
%U 128,138,149,160,172,186,200,214,230,248,266,285,308,327,348,373,400,429
%N Number of partitions of n into distinct odious numbers.
%H Alois P. Heinz, <a href="/A116492/b116492.txt">Table of n, a(n) for n = 0..10000</a> (first 1001 terms from Andrew Howroyd)
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F Weigh Transform of characteristic function of A000069.
%p g:= proc(n) option remember; is(add(i, i=Bits[Split](n))::odd) end:
%p b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0, 1,
%p b(n, i-1)+`if`(g(i), b(n-i, min(n-i, i-1)), 0)))
%p end:
%p a:= n-> b(n$2):
%p seq(a(n), n=0..100); # _Alois P. Heinz_, Sep 08 2019
%t seq[n_] := Product[If[OddQ[Total[DigitCount[Abs[k], 2, 1]]], 1 + x^k, 1], {k, 1, n}] + O[x]^n // CoefficientList[#, x]&;
%t seq[100] (* _Jean-François Alcover_, Sep 08 2019 *)
%o (PARI) seq(n)={Vec(prod(k=1, n, if(hammingweight(k)%2==1, 1+x^k, 1) + O(x*x^n)))} \\ _Andrew Howroyd_, Jun 22 2018
%Y Cf. A067590, A116491.
%K nonn
%O 0,8
%A _Christian G. Bower_, Feb 17 2006
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