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A350674 Irregular table read by rows; the n-th row contains, in weakly decreasing order, the positive squares summing to n as obtained by the greedy algorithm.

%I A350674 #12 Jan 05 2024 13:44:25
%S A350674 1,1,1,1,1,1,4,4,1,4,1,1,4,1,1,1,4,4,9,9,1,9,1,1,9,1,1,1,9,4,9,4,1,9,
%T A350674 4,1,1,16,16,1,16,1,1,16,1,1,1,16,4,16,4,1,16,4,1,1,16,4,1,1,1,16,4,4,
%U A350674 25,25,1,25,1,1,25,1,1,1,25,4,25,4,1,25,4,1,1
%N A350674 Irregular table read by rows; the n-th row contains, in weakly decreasing order, the positive squares summing to n as obtained by the greedy algorithm.
%C A350674 The n-th row has A053610(n) terms.
%H A350674 Andrew Howroyd, <a href="/A350674/b350674.txt">Table of n, a(n) for n = 1..1733</a> (rows 1..500)
%F A350674 T(n, 1) = A048760(n).
%F A350674 T(n, A053610(n)) = A350698(n).
%e A350674 The first rows are:
%e A350674      1:    [1]
%e A350674      2:    [1, 1]
%e A350674      3:    [1, 1, 1]
%e A350674      4:    [4]
%e A350674      5:    [4, 1]
%e A350674      6:    [4, 1, 1]
%e A350674      7:    [4, 1, 1, 1]
%e A350674      8:    [4, 4]
%e A350674      9:    [9]
%e A350674     10:    [9, 1]
%e A350674     11:    [9, 1, 1]
%e A350674     12:    [9, 1, 1, 1]
%e A350674     13:    [9, 4]
%e A350674     14:    [9, 4, 1]
%e A350674     15:    [9, 4, 1, 1]
%e A350674     16:    [16]
%o A350674 (PARI) row(n,e=2) = { my (g=[], r); while (n, r=sqrtnint(n,e); n-=r^e; g=concat(g,[r^e])); g }
%Y A350674 Cf. A007961, A048760, A053610, A350698.
%K A350674 nonn,tabf
%O A350674 1,7
%A A350674 _Rémy Sigrist_, Jan 10 2022