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%I #8 Sep 21 2018 02:21:18
%S 1,1,0,1,1,1,1,1,2,2,3,4,8,11,18,31,48,79,123,203,315,514,791,1278,
%T 1983,3169,4922,7832,12206,19333,30215,47757,74816,118125,185423,
%U 292674,460279,726599,1144508,1807639,2851366,4506371,7117308
%N "DHK" (bracelet, identity, unlabeled) transform of 1,0,1,0,... (odd).
%H Andrew Howroyd, <a href="/A032243/b032243.txt">Table of n, a(n) for n = 0..500</a>
%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%o (PARI)
%o DHK(p,n)={my(q=((1+p)^2/(1-subst(p, x, x^2))-1)/2); p + (p^2-subst(p, x, x^2))/2 + sum(d=1, n, moebius(d)*(log(subst(1/(1+O(x*x^(n\d))-p), x, x^d))/d - subst(q + O(x*x^(n\d)), x, x^d)))/2}
%o seq(n)=Vec(1 + DHK(x/(1-x^2) + O(x*x^n), n)) \\ _Andrew Howroyd_, Sep 21 2018
%K nonn
%O 0,9
%A _Christian G. Bower_
%E a(0)=1 prepended by _Andrew Howroyd_, Sep 21 2018
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