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reviewed
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proposed
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a[n_] := PowersRepresentations[n, 10, 2] // Length; Array[a, 120, 0] (* Jean-François Alcover, Feb 19 2016 *)
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b:= proc(n, i, t) option remember; `if`(n=0, 1,
`if`(i<1 or t<1, 0, b(n, i-1, t)+
`if`(i^2>n, 0, b(n-i^2, i, t-1))))
end:
a:= n-> b(n, isqrt(n), 10):
seq(a(n), n=0..120); # Alois P. Heinz, May 30 2014
Alois P. Heinz, <a href="/A025425/b025425.txt">Table of n, a(n) for n = 0..10000</a>
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Cf. A001156.
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_David W. Wilson (davidwwilson(AT)comcast.net)_