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A157927 Joint-rank array of the numbers i^2+j^2, where i>=0, j>=0.

%I A157927 #17 Apr 26 2016 11:36:58
%S A157927 1,2,2,4,3,4,7,5,5,7,10,8,6,8,10,14,11,9,9,11,14,19,15,13,12,13,15,19,
%T A157927 24,20,16,14,14,16,20,24,30,25,21,18,17,18,21,25,30,37,31,27,23,22,22,
%U A157927 23,27,31,37,44,38,32,28,26,25,26,28,32,38,44
%N A157927 Joint-rank array of the numbers i^2+j^2, where i>=0, j>=0.
%C A157927 The definition of joint-rank array given at A182801 is
%C A157927 here extended to arrays R={f(i,j)} for which the numbers
%C A157927 f(i,j) are not necessarily distinct.  Specifically, all
%C A157927 duplicates are assigned the same rank when all the numbers
%C A157927 in R are jointly ranked.  Let {a(i,j)} denote the
%C A157927 resulting joint-rank array.  In case all f(i,j) are
%C A157927 positive integers, a(i,j)=f(i,j)-L(i,j), where L(i,j) is
%C A157927 the number of numbers in R that are <=f(i,j).
%C A157927 (Row 1)=A047808.
%e A157927 A corner of the array R={i^2+j^2} is
%e A157927 0....1....4....9...16...
%e A157927 1....2....5...10...17...
%e A157927 4....5....8...13...20...
%e A157927 9...10...13...18...25...
%e A157927 Replace each term of R by its rank:
%e A157927 1....2....4....7...10...
%e A157927 2....3....5....8...11...
%e A157927 4....5....6....9...13...
%e A157927 7....8....9...12...14...
%Y A157927 Cf. A182801, A048147.
%K A157927 nonn,tabl
%O A157927 1,2
%A A157927 _Clark Kimberling_, Dec 17 2010