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A353589
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Number of nondecreasing nonnegative integer quadruples (m,p,q,r) such that m^2 + p^2 + q^2 + r^2 = n^2 and m +- p +- q +- r = +- n.
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3
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1, 1, 2, 2, 2, 2, 4, 2, 2, 4, 4, 4, 4, 3, 4, 6, 2, 5, 8, 5, 4, 6, 8, 5, 4, 7, 6, 9, 4, 6, 12, 6, 2, 12, 10, 9, 8, 7, 10, 10, 4, 9, 12, 9, 8, 17, 10, 9, 4, 9, 14, 16, 6, 10, 18, 17, 4, 16, 12, 12, 12, 11, 12, 17, 2, 16, 24, 13, 10, 18, 18, 13, 8, 14, 14, 26, 10, 17, 20, 14, 4, 23
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OFFSET
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0,3
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COMMENTS
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LINKS
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EXAMPLE
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For n = 1, (0, 0, 0, 1) is the only solution.
For n = 2, (0, 0, 0, 2) and (1, 1, 1, 1) are solutions, with 1 + 1 + 1 - 1 = 2.
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PROG
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(PARI) apply( {A353589(n, show=0, cnt=0, n2=n^2, e=[1, -1]~)=
for(a=0, sqrtint(n2\4), for(b=a, sqrtint((n2-a^2)\3),
my(s=[a+b, b-a, a-b, -a-b]); foreach(sum2sqr(n2-a^2-b^2), cd, cd[1] >= b &&
vecsum(cd)+s[1] >= n && foreach(s, d, (vecsum(cd)+d==n || abs(cd*e+d)==n)&&
cnt++&& !(show && print1(concat([a, b], cd)))&& break)))); cnt}, [0..99]) \\ See A133388 for sum2sqr().
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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