%I #9 Mar 30 2012 16:52:03
%S 3,2,1,0,4,2,1,0,4,3,1,0,4,3,2,0,4,3,2,1,5,2,1,0,5,3,1,0,5,3,2,0,5,3,
%T 2,1,5,4,1,0,5,4,2,0,5,4,2,1,5,4,3,0,5,4,3,1,5,4,3,2,6,2,1,0,6,3,1,0,
%U 6,3,2,0,6,3,2,1,6,4,1,0,6,4,2,0,6,4,2,1,6,4,3,0,6,4,3,1,6,4,3,2,6,5,1,0,6,5,2,0,6,5,2,1,6,5,3,0,6,5,3,1,6
%N Write n = C(i,4)+C(j,3)+C(k,2)+C(l,1) with i>j>k>l>=0; let L[n] = [i,j,k,l]; sequence gives list of quadruples L[n], n >= 0.
%C Each n >= 0 has a unique representation as n = C(i,4)+C(j,3)+C(k,2)+C(l.1) with i>j>k>l>=0. This is the combinatorial number system of degree t = 4, where we get [A194882, A194883, A194884, A127324]. For degree t = 3 see A194847.
%D D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, Section 7.2.1.3, Eq. (20), p. 360.
%e List of quadruples begins:
%e [3, 2, 1, 0]
%e [4, 2, 1, 0]
%e [4, 3, 1, 0]
%e [4, 3, 2, 0]
%e [4, 3, 2, 1]
%e [5, 2, 1, 0]
%e [5, 3, 1, 0]
%e [5, 3, 2, 0]
%e [5, 3, 2, 1]
%e [5, 4, 1, 0]
%e [5, 4, 2, 0]
%e ...
%Y The four columns are [A194882, A194883, A194885, A127324], or equivalently [A127321+3, A127322+2, A127323+1, A127324].
%K nonn,tabf
%O 0,1
%A _N. J. A. Sloane_, Sep 04 2011