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Express n as the sum of four squares, x^2+y^2+z^2+w^2, x>=y>=z>=w>=0, minimizing the value of x, then minimizing y for that x. a(n) is that y.
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%I #2 Mar 30 2012 17:35:16

%S 0,0,1,1,1,1,1,1,2,2,2,1,2,2,2,2,2,2,2,3,3,2,3,3,2,2,3,3,3,3,3,3,4,3,

%T 3,3,3,4,3,3,4,4,4,3,3,4,4,3,4,4,4,4,4,3,4,5,4,4,4,4,5,4,4,5,4,4,4,5,

%U 5,4,5,5,4,4,5,5,5,4,5,5,6,5,5,4,5,6,5,5,6,6,5,5,6,5,5,5,4,6,6,5,5,6,5,5,6

%N Express n as the sum of four squares, x^2+y^2+z^2+w^2, x>=y>=z>=w>=0, minimizing the value of x, then minimizing y for that x. a(n) is that y.

%e 10 = 2^2 + 2^2 + 1^2 + 1^2, so a(10) = 2. The only representation for 11 is 3^2 + 1^2 + 1^2 + 0^2, so a(11) = 1.

%Y Cf. A122921, A122923, A122924.

%K nonn

%O 0,9

%A _Franklin T. Adams-Watters_, Sep 19 2006