%I #18 Oct 23 2019 23:28:35
%S 0,0,1,1,0,1,1,2,2,2,0,1,1,2,2,2,3,3,3,3,0,1,1,2,2,2,3,3,3,3,4,4,4,4,
%T 4,0,1,1,2,2,2,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,0,1,1,2,2,2,3,3,3,3,4,4,
%U 4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,6,0,1,1,2,2,2,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5
%N Second tetrahedral coordinate.
%C If {(X,Y,Z)} are triples of nonnegative integers with X >= Y >= Z ordered by X, Y and Z, then X=A056556(n), Y=A056557(n) and Z=A056558(n)
%F a(n) = floor((sqrt(8*(n-A056556(n)*(A056556(n)+1)*(A056556(n)+2)/6)+1)-1)/2) = A003056(n-A000292(A056556(n)-1)).
%F a(n+1) = 0 if A056556(n) = A056558(n); a(n+1) = a(n)+1 if a(n) = A056558(n); otherwise a(n+1) = a(n). - _Graeme McRae_, Jan 09 2007
%Y Cf. A000292, A002262, A003056, A056556, A056558, A056559, A056560.
%Y See also A194847, A194848.
%K nonn
%O 0,8
%A _Henry Bottomley_, Jun 26 2000