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%I #14 Nov 08 2020 04:27:28
%S 1,1,1,1,1,3,1,7,1,31,123,151,121,897,7351,5415,14881,48705,150583,
%T 468973,1013163,1432471,1730023,50432107,14925241,125269841,74592537,
%U 241763479,213156871,895153173,7716880623,2681163865,3190865761,22501985413,116279718801
%N Number of compositions (ordered partitions) of n^2 into distinct squares.
%H Alois P. Heinz, <a href="/A331884/b331884.txt">Table of n, a(n) for n = 0..300</a>
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F a(n) = A331844(A000290(n)).
%e a(5) = 3 because we have [25], [16, 9] and [9, 16].
%p b:= proc(n, i, p) option remember;
%p `if`(i*(i+1)*(2*i+1)/6<n, 0, `if`(n=0, p!,
%p `if`(i^2>n, 0, b(n-i^2, i-1, p+1))+b(n, i-1, p)))
%p end:
%p a:= n-> b(n^2, n, 0):
%p seq(a(n), n=0..35); # _Alois P. Heinz_, Jan 30 2020
%t b[n_, i_, p_] := b[n, i, p] = If[i(i+1)(2i+1)/6 < n, 0, If[n == 0, p!, If[i^2 > n, 0, b[n - i^2, i - 1, p + 1]] + b[n, i - 1, p]]];
%t a[n_] := b[n^2, n, 0];
%t a /@ Range[0, 35] (* _Jean-François Alcover_, Nov 08 2020, after _Alois P. Heinz_ *)
%Y Cf. A000290, A006456, A030273, A032020, A037444, A105152, A224366, A232173, A280129, A298640, A331844.
%K nonn
%O 0,6
%A _Ilya Gutkovskiy_, Jan 30 2020
%E a(24)-a(34) from _Alois P. Heinz_, Jan 30 2020
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