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A298640 Number of compositions (ordered partitions) of n^2 into squares > 1.

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