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A095861
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Number of primitive Pythagorean triangles of form (X,Y,Y+1) with hypotenuse Y+1 less than or equal to n.
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2
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0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6
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OFFSET
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1,13
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COMMENTS
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Indices where records occur are hypotenuse values A001844 (Y+1); corresponding leg values given by A046092 (Y) and A005408 (X).
The number k, for k >= 0, appears exactly 4*(k+1) = A008586(k+1) times. The number k appears for the first time for a(4*T(k) + 1) = a(A001844(k)), where T(k) = A000217(k); see the preceding comment on records. - Wolfdieter Lang, Mar 01 2022
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LINKS
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FORMULA
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a(n) = floor((sqrt(2*n-1) - 1)/2).
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MAPLE
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A095861 := proc (x) local y; y := 0; while (2*y+2)*(y+2) <= x do y := y+1 end do; return y end proc; map(A095861, [seq(k, k = 0 .. 100)]) # Stephen Crowley, Aug 01 2009
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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