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A224982 Numbers that are the sum of exactly 7 distinct nonzero squares.

%I A224982 #8 Nov 20 2021 09:35:33
%S A224982 140,155,168,172,179,185,188,191,195,196,200,203,204,205,211,212,215,
%T A224982 217,219,220,224,225,227,230,231,232,233,235,236,239,240,243,244,245,
%U A224982 246,247,248,251,252,254,256,257,259,260,263,264,265,267,268,269,270,271
%N A224982 Numbers that are the sum of exactly 7 distinct nonzero squares.
%H A224982 Reinhard Zumkeller, <a href="/A224982/b224982.txt">Table of n, a(n) for n = 1..1000</a>
%H A224982 Paul T. Bateman, Adolf J. Hildebrand, and George B. Purdy, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa67/aa6745.pdf">Sums of distinct squares</a>, Acta Arithmetica 67 (1994), pp. 349-380.
%H A224982 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%e A224982 a(1) = 1 + 4 + 9 + 16 + 25 + 36 + 49 = 140 = A000330(7);
%e A224982 a(2) = 1 + 4 + 9 + 16 + 25 + 36 + 64 = 155;
%e A224982 a(3) = 1 + 4 + 9 + 16 + 25 + 49 + 64 = 168;
%e A224982 a(4) = 1 + 4 + 9 + 16 + 25 + 36 + 81 = 172;
%e A224982 a(5) = 1 + 4 + 9 + 16 + 36 + 49 + 64 = 179.
%t A224982 nmax = 1000;
%t A224982 S[n_] := S[n] = Union[Total /@ Subsets[
%t A224982      Range[Floor[Sqrt[n]]]^2, {7}]][[1 ;; nmax]];
%t A224982 S[nmax];
%t A224982 S[n = nmax + 1];
%t A224982 While[S[n] != S[n - 1], n++];
%t A224982 S[n] (* _Jean-François Alcover_, Nov 20 2021 *)
%o A224982 (Haskell)
%o A224982 a224982 n = a224982_list !! (n-1)
%o A224982 a224982_list = filter (p 7 $ tail a000290_list) [1..] where
%o A224982    p k (q:qs) m = k == 0 && m == 0 ||
%o A224982                   q <= m && k >= 0 && (p (k - 1) qs (m - q) || p k qs m)
%Y A224982 Cf. A003995, A004431, A004432, A004433, A004434, A224981, A224983, A000290.
%K A224982 nonn
%O A224982 1,1
%A A224982 _Reinhard Zumkeller_, Apr 22 2013