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%I #11 Jul 11 2018 06:39:48
%S 0,0,0,0,0,0,1,2,3,3,5,6,8,11,12,14,18,20,25,27,31,35,42,46,50,55,61,
%T 67,74,78,87,94,101,111,118,124,133,143,153,159,172,181,193,206,214,
%U 227,240,251,265,277,290,303,322,337,350,363,378,392,410,421,440,461
%N Number of sums i^2 + j^2 that occur more than once for 1 <= i <= j <= n.
%C If the {s+t} sums are generated by addition 2 terms of an S set consisting of n different entries, then at least 1 and at most n(n+1)/2=A000217(n) distinct values can be obtained. The set of first n squares gives results falling between these two extremes.
%e S={1,4,9,...,100,121} provides 61 different sums of two (not necessarily different) squares: {2,5,8,..,202,221,242}. Only 5 of these sums arise more than once:
%e 50 = 1 + 49 = 25 + 25;
%e 65 = 1 + 64 = 16 + 49;
%e 85 = 4 + 81 = 36 + 49;
%e 125 = 4 + 121 = 25 + 100;
%e 130 = 9 + 121 = 49 + 81.
%e Therefore a(11) = (12*11/2) - 61 = 5.
%t f[x_] := x^2 t0=Table[Length[Union[Flatten[Table[f[u]+f[w], {w, 1, m}, {u, 1, m}]]]], {m, 1, 75}] t1=Table[(w*(w+1)/2)-Part[t0, w], {w, a, b}]
%Y Cf. A000217.
%K nonn
%O 1,8
%A _Labos Elemer_, Jun 22 2001
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