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%I #72 Apr 18 2019 22:04:30
%S 1,0,0,1,1,0,0,0,1,0,0,0,1,1,0,1,0,0,0,0,0,0,0,0,2,0,0,0,1,1,0,0,0,0,
%T 0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,0,0,0,1,0,0,1,0,0,0,0,
%U 0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,1,0,0,0,1,1
%N a(n) = number of partitions of n into consecutive positive squares.
%H Seiichi Manyama, <a href="/A296338/b296338.txt">Table of n, a(n) for n = 1..10000</a>
%F a(A034705(n)) >= 1 for n > 1.
%F G.f.: Sum_{i>=1} Sum_{j>=i} Product_{k=i..j} x^(k^2). - _Ilya Gutkovskiy_, Apr 18 2019
%e 1 = 1^2, so a(1) = 1.
%e 4 = 2^2, so a(4) = 1.
%e 5 = 1^2 + 2^2, so a(5) = 1.
%e 9 = 3^2, so a(9) = 1.
%e 13 = 2^2 + 3^2, so a(13) = 1.
%e 14 = 1^2 + 2^2 + 3^2, so a(14) = 1.
%e 16 = 4^2, so a(16) = 1.
%e 25 = 3^2 + 4^2 = 5^2, so a(25) = 2.
%e 29 = 2^2 + 3^2 + 4^2, so a(29) = 1.
%e 30 = 1^2 + 2^2 + 3^2 + 4^2, so a(30) = 1.
%t nMax = 100; t = {0}; Do[k = n; s = 0; While[s = s + k^2; s <= nMax, AppendTo[t, s]; k++], {n, 1, nMax}]; tt = Tally[t]; a[_] = 0; Do[a[tt[[i, 1]]] = tt[[i, 2]], {i, 1, Length[tt]}]; Table[a[n], {n, 1, nMax}] (* _Jean-François Alcover_, Feb 04 2018, using _T. D. Noe_'s program for A034705 *)
%o (Ruby)
%o def A296338(n)
%o m = Math.sqrt(n).to_i
%o ary = Array.new(n + 1, 0)
%o (1..m).each{|i|
%o sum = i * i
%o ary[sum] += 1
%o i += 1
%o sum += i * i
%o while sum <= n
%o ary[sum] += 1
%o i += 1
%o sum += i * i
%o end
%o }
%o ary[1..-1]
%o end
%o p A296338(100)
%Y Cf. A000290, A001227, A034705, A130052, A234304, A297199, A298467, A299173.
%K nonn
%O 1,25
%A _Seiichi Manyama_, Jan 14 2018
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