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%I #15 May 21 2018 02:58:39
%S 1,0,1,1,2,8,12,129,874,9630,167001,3043147,72844510,2423789655,
%T 106665874384,6156805673648,470151743582651,47558937432498729,
%U 6363358599941131580,1126147544855148769425,263646401550138303553708,81649922556593759124887197
%N Number of compositions (ordered partitions) of n^2 into squares > 1.
%H Alois P. Heinz, <a href="/A298640/b298640.txt">Table of n, a(n) for n = 0..128</a>
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F a(n) = [x^(n^2)] 1/(1 - Sum_{k>=2} x^(k^2)).
%F a(n) = A280542(A000290(n)).
%e a(5) = 8 because we have [25], [16, 9], [9, 16], [9, 4, 4, 4, 4], [4, 9, 4, 4, 4], [4, 4, 9, 4, 4], [4, 4, 4, 9, 4] and [4, 4, 4, 4, 9].
%p b:= proc(n) option remember; `if`(n=0, 1,
%p add(b(n-j^2), j=2..isqrt(n)))
%p end:
%p a:= n-> b(n^2):
%p seq(a(n), n=0..25); # _Alois P. Heinz_, Feb 05 2018
%t b[n_] := b[n] = If[n == 0, 1, Sum[b[n - j^2], {j, 2, Floor @ Sqrt[n]}]];
%t a[n_] := b[n^2];
%t Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, May 21 2018, after _Alois P. Heinz_ *)
%Y Cf. A000290, A006456, A078134, A224366, A280542, A298642.
%K nonn
%O 0,5
%A _Ilya Gutkovskiy_, Jan 24 2018
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