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A025442 Number of partitions of n into 3 distinct nonzero squares. 20
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 1, 1, 0, 0, 2, 1, 0, 0, 0, 2, 1, 0, 2, 1, 0, 0, 1, 0, 1, 1, 0, 2, 0, 0, 2, 2, 1, 0, 1, 2, 0, 0, 0, 2, 0, 0, 3, 0, 0, 1, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,63
LINKS
FORMULA
a(n)>0 <=> n is in A004432. - M. F. Hasler, Feb 03 2013
a(n) = [x^n y^3] Product_{k>=1} (1 + y*x^(k^2)). - Ilya Gutkovskiy, Apr 22 2019
MAPLE
b:= proc(n, i, t) option remember; `if`(n=0, `if`(t=0, 1, 0),
`if`(i<1 or t<1, 0, `if`(i=1, 0, b(n, i-1, t))+
`if`(i^2>n, 0, b(n-i^2, i-1, t-1))))
end:
a:= n-> b(n, isqrt(n), 3):
seq(a(n), n=0..120); # Alois P. Heinz, Feb 07 2013
MATHEMATICA
b[n_, i_, t_] := b[n, i, t] = If[n==0, If[t==0, 1, 0], If[i<1 || t<1, 0, If[i==1, 0, b[n, i-1, t]] + If[i^2 > n, 0, b[n-i^2, i-1, t-1]]]]; a[n_] := b[n, Sqrt[n] // Floor, 3]; Table[a[n], {n, 0, 120}] (* Jean-François Alcover, Oct 10 2015, after Alois P. Heinz *)
PROG
(PARI) A025442(n)={sum(x=1, sqrtint(n\3), sum(y=x+1, sqrtint((n-1-x^2)\2), issquare(n-x^2-y^2)))} \\ - M. F. Hasler, Feb 03 2013
CROSSREFS
Column k=3 of A341040.
Sequence in context: A159708 A144625 A224772 * A260118 A128582 A213185
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified April 12 14:01 EDT 2024. Contains 371635 sequences. (Running on oeis4.)