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%I #37 Nov 01 2023 20:50:51
%S 0,0,1,0,1,0,2,1,0,2,1,0,3,2,1,0,3,2,1,0,4,3,2,1,0,4,3,2,1,0,5,4,3,2,
%T 1,0,5,4,3,2,1,0,6,5,4,3,2,1,0,6,5,4,3,2,1,0,7,6,5,4,3,2,1,0,7,6,5,4,
%U 3,2,1,0,8,7,6,5,4,3,2,1,0,8,7,6,5,4,3
%N The sequence used to represent partition binary diagram as an array.
%C This sequence differs from A025672 first at index n=110.
%H Mircea Merca, <a href="http://dx.doi.org/10.1093/comjnl/bxs111">Binary Diagrams for Storing Ascending Compositions</a>, Comp. J., 2012.
%F a(n) = floor((1/4)*ceiling(sqrt(4*n))^2) - n.
%F a(n^2) = a(n^2+n) = 0.
%F From _Szymon Lukaszyk_, Oct 27 2023: (Start)
%F a(n) = (-n) mod round(sqrt(n)).
%F a(n) = (A167268(n) - 2)/4. (End)
%p seq(floor((1/4)*ceil(sqrt(4*n))^2)-n,n=1..50)
%o (PARI) A216607(n)=floor((1/4)*ceil(sqrt(4*n))^2)-n;
%Y Cf. A025672, A167268.
%K nonn,easy
%O 1,7
%A _Mircea Merca_, Sep 10 2012
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