Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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