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%I #18 Oct 27 2017 21:58:47
%S 18,25,26,27,28,33,37,38,41,43,51,53,55,59,60,62,72,79,92,95,104,112,
%T 152,240,248,288,368,416,448,608,960,992,1152,1472,1664,1792,2432,
%U 3840,3968,4608,5888,6656,7168,9728,15360,15872,18432,23552,26624,28672
%N Integers with precisely three partitions into sums of four squares of nonnegative numbers.
%C A002635(a(n)) = 3.
%H Robert Price, <a href="/A245022/b245022.txt">Table of n, a(n) for n = 1..55</a>
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%e a(1) = 18 = 16 + 1 + 1 + 0 = 9 + 9 + 0 + 0 = 9 + 4 + 4 + 1;
%e a(2) = 25 = 25 + 0 + 0 + 0 = 16 + 9 + 0 + 0 = 16 + 4 + 4 + 1;
%e a(3) = 26 = 25 + 1 + 0 + 0 = 16 + 9 + 1 + 0 = 9 + 9 + 4 + 4;
%e a(4) = 27 = 25 + 1 + 1 + 0 = 16 + 9 + 1 + 1 = 9 + 9 + 9 + 0;
%e a(5) = 28 = 25 + 1 + 1 + 1 = 16 + 4 + 4 + 4 = 9 + 9 + 9 + 1;
%e a(6) = 33 = 25 + 4 + 4 + 0 = 16 + 16 + 1 + 0 = 16 + 9 + 4 + 4;
%e a(7) = 37 = 36 + 1 + 0 + 0 = 25 + 4 + 4 + 4 = 16 + 16 + 4 + 1;
%e a(8) = 38 = 36 + 1 + 1 + 0 = 25 + 9 + 4 + 0 = 16 + 9 + 9 + 4;
%e a(9) = 41 = 36 + 4 + 1 + 0 = 25 + 16 + 0 + 0 = 16 + 16 + 9 + 0;
%e a(10) = 43 = 25 + 16 + 1 + 1 = 25 + 9 + 9 + 0 = 16 + 9 + 9 + 9;
%e a(11) = 51 = 49 + 1 + 1 + 0 = 25 + 25 + 1 + 0 = 25 + 16 + 9 + 1;
%e a(12) = 53 = 49 + 4 + 0 + 0 = 36 + 16 + 1 + 0 = 36 + 9 + 4 + 4.
%t Select[ Range@ 30000, Length@PowersRepresentations[#, 4, 2] == 3 &] (* _Robert G. Wilson v_, Oct 27 2017 *)
%o (Haskell)
%o a245022 n = a245022_list !! (n-1)
%o a245022_list = filter ((== 3) . a002635) [0..]
%Y Cf. A002635, A006431, A180149.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Jul 13 2014
%E a(44)-a(50) from _Robert Price_, Oct 26 2017
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