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A175958
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Number of partitions of n^2 into 4 distinct nonzero squares.
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2
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0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 1, 5, 0, 4, 4, 5, 0, 10, 4, 7, 0, 11, 7, 17, 1, 13, 17, 15, 0, 29, 13, 27, 4, 23, 17, 41, 0, 29, 35, 32, 4, 66, 24, 38, 0, 47, 35, 73, 7, 50, 56, 73, 1, 91, 42, 63, 17, 68, 49, 125, 0, 103, 93, 83, 13, 133, 86, 93, 4
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OFFSET
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0,14
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LINKS
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FORMULA
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EXAMPLE
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a(9)=1 refers to the partition 9^2 = 2^2+4^2+5^2+6^2. a(11)=1 refers to 11^2 = 1^2+2^2+4^2+10^2. a(13)=2 refers to 13^2 = 1^2+2^2+8^2+10^2 = 2^2+4^2+7^2+10^2.
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MAPLE
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A025443 := proc(n) local res, a, b, c, d ; res := 0 ; for a from 1 do if 4*a^2 > n then break; fi; for b from a+1 do if a^2+3*b^2 > n then break; fi; for c from b+1 do if a^2+b^2+2*c^2 > n then break; fi; for d from c+1 do if a^2+b^2+c^2+d^2 > n then break; elif a^2+b^2+c^2+d^2 = n then res := res+1 ; fi ; end do; end do; end do: end do: res ; end proc:
A := proc(n) A025443(n^2) ; end proc: seq(A(n), n=0..60) ;
# second Maple program:
b:= proc(n, i, t) option remember; `if`(n=0, `if`(t=0, 1, 0),
`if`(t*i^2<n, 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^2, n, 4):
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MATHEMATICA
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b[n_, i_, t_] := b[n, i, t] = If[n == 0, If[t == 0, 1, 0], If[t*i^2 < n, 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^2, n, 4]; Table[a[n], {n, 0, 80}] (* Jean-François Alcover, Jun 24 2015, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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