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A240952 Smallest number that can be written in exactly n ways as sum of two quarter-squares.

%I A240952 #17 Jul 08 2021 09:54:08
%S A240952 19,0,1,2,6,18,36,72,106,450,562,2312,1156,9522,1381,8712,4930,16562,
%T A240952 13812,35912,14862,233928,53316,361250,40056,211250,55981,1678112,
%U A240952 51106,1216800,305256,610512,255531
%N A240952 Smallest number that can be written in exactly n ways as sum of two quarter-squares.
%C A240952 A245575(a(n)) = n and A245575(a(m)) <> n for m < a(n).
%e A240952 a(0) = A245585(1) = 19, A245575(19) = 0;
%e A240952 a(1) =  0: A245575(0) =  #{0+0} = 1;
%e A240952 a(2) =  1: A245575(1) =  #{1+0, 0+1} = 2;
%e A240952 a(3) =  2: A245575(2) =  #{2+0, 1+1, 0+2} = 3;
%e A240952 a(4) =  6: A245575(6) =  #{6+0, 4+2, 2+4, 0+6} = 4;
%e A240952 a(5) = 18: A245575(18) = #{16+2, 12+6, 9+9, 6+12, 2+16} = 5;
%e A240952 a(6) = 36: A245575(36) = #{36+0, 30+6, 20+16, 16+20, 6+30, 0+36} = 6.
%t A240952 nmax = 36000;
%t A240952 qsQ[n_] := qsQ[n] = With[{s = Sqrt[n]}, Which[IntegerQ[s], True, n == Floor[s] (Floor[s]+1), True, True, False]];
%t A240952 A245575[n_] := Count[Range[0, n], k_ /; qsQ[k] && qsQ[n-k]];
%t A240952 Table[{A245575[n], n}, {n, 0, nmax}] // Sort // SplitBy[#, First]& // #[[All, 1, 2]]& (* _Jean-François Alcover_, May 08 2017 *)
%o A240952 (Haskell)
%o A240952 import Data.List (elemIndex); import Data.Maybe (fromJust)
%o A240952 a240952 = fromJust . (`elemIndex` a245575_list)
%Y A240952 Cf. A002620, A245575, A245585.
%K A240952 nonn,more
%O A240952 0,1
%A A240952 _Reinhard Zumkeller_, Aug 04 2014
%E A240952 a(21)-a(32) from _Jinyuan Wang_, Jul 08 2021