OFFSET
0,5
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..250
EXAMPLE
n=10: 10^2 = 100 = 64+36 = 36+16+16+16+16 = 25+25+25+25, all other partitions of 100 into squares contain parts < 10, therefore a(10) = 4.
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1,
`if`(i^2>n, 0, b(n, i+1) +b(n-i^2, i)))
end:
a:= proc(n) local r; r:= isqrt(n);
b(n^2, r+`if`(r^2<n, 1, 0))
end:
seq(a(n), n=0..50); # Alois P. Heinz, Apr 15 2013
MATHEMATICA
b[n_, i_] := b[n, i] = If[n==0, 1, If[i^2>n, 0, b[n, i+1] + b[n-i^2, i]]]; a[n_] := With[{r = Sqrt[n]//Floor}, b[n^2, r + If[r^2<n, 1, 0]]]; Table[ a[n], {n, 0, 50}] (* Jean-François Alcover, Oct 26 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Mar 21 2004
STATUS
approved