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%I #36 Nov 30 2019 01:30:38
%S 1,2,1,3,1,4,2,1,5,2,1,6,3,2,1,7,3,2,1,8,4,3,2,1,9,4,3,2,1,10,5,4,3,2,
%T 1,11,5,4,3,2,1,12,6,5,4,3,2,1,13,6,5,4,3,2,1,14,7,6,5,4,3,2,1,15,7,6,
%U 5,4,3,2,1,16,8,7,6,5,4,3,2,1
%N The sequence of the parts in the partition binary diagram represented as an array.
%C n is followed by the sequence floor(n/2), floor(n/2)-1, ..., 1.
%D Mircea Merca, Binary Diagrams for Storing Ascending Compositions, Comp. J., 2012, (DOI 10.1093/comjnl/bxs111)
%F If n=k^2 or n=k^2+k then a(n) = ceiling(sqrt(4*n))-1, otherwise a(n) = floor((ceiling(sqrt(4*n))^2)/4) - n.
%e 1,
%e 2, 1,
%e 3, 1,
%e 4, 2, 1,
%e 5, 2, 1,
%e 6, 3, 2, 1,
%e 7, 3, 2, 1,
%e 8, 4, 3, 2, 1,
%e 9, 4, 3, 2, 1,
%e 10, 5, 4, 3, 2, 1,
%e 11, 5, 4, 3, 2, 1,
%e 12, 6, 5, 4, 3, 2, 1,
%e 13, 6, 5, 4, 3, 2, 1,
%e 14, 7, 6, 5, 4, 3, 2, 1,
%e 15, 7, 6, 5, 4, 3, 2, 1,
%e 16, 8, 7, 6, 5, 4, 3, 2, 1
%p seq(piecewise(floor((1/4)*ceil(sqrt(4*n))^2)-n = 0, ceil(sqrt(4*n))-1, 0 < floor((1/4)*ceil(sqrt(4*n))^2)-n, floor((1/4)*ceil(sqrt(4*n))^2)-n),n=1..50)
%t Table[{n,Range[Floor[n/2],1,-1]},{n,20}]//Flatten (* _Harvey P. Dale_, Jul 16 2017 *)
%K nonn
%O 1,2
%A _Mircea Merca_, Sep 10 2012
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