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A309395
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Number of integer-sided triangles with sides a,b,c, max(a,b) < c, a + c = n that are right triangles.
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1
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0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 3, 4, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 2, 0, 0, 0, 0, 1, 4, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 3, 0, 6, 1, 4
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OFFSET
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1,18
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LINKS
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FORMULA
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a(n) > 0 if and only if n is a term in A046790.
a(n^2) = floor((n-1)/2) = A004526(n-1).
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EXAMPLE
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n | (a,b,c)
-----+-----------------------------------------
8 | [ 3, 4, 5]
9 | [ 4, 3, 5]
16 | [ 6, 8, 10]
18 | [ 5, 12, 13], [ 8, 6, 10]
24 | [ 9, 12, 15]
25 | [ 8, 15, 17], [12, 5, 13]
27 | [12, 9, 15]
32 | [ 7, 24, 25], [12, 16, 20], [15, 8, 17]
36 | [10, 24, 26], [16, 12, 20]
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PROG
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(PARI) {a(n) = sum(k=n\2+1, n-1, issquare(k^2-(n-k)^2))}
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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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