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A095861 Number of primitive Pythagorean triangles of form (X,Y,Y+1) with hypotenuse Y+1 less than or equal to n. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,13

COMMENTS

Where records occur gives hypotenuse values A001844 (Y+1); corresponding leg values given by A046092 (Y) and A005408 (X).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

S. Crowley, Mellin and Laplace Integral Transforms Related to the Harmonic Sawtooth Map and a Diversion Into The Theory Of Fractal Strings, vixra:1202.0079, 2012.

S. Crowley, Integral Transforms of the Harmonic Sawtooth Map, The Riemann Zeta Function, Fractal Strings, and a Finite Reflection Formula, arXiv preprint arXiv:1210.5652 [math.NT], 2012. - N. J. A. Sloane, Jan 01 2013

Eric Weisstein's World of Mathematics, Pythagorean Triple.

FORMULA

a(n) = floor((sqrt(2*n-1) - 1)/2).

MAPLE

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

MATHEMATICA

Table[Floor[(Sqrt[2*n-1] - 1)/2], {n, 1, 100}] (* Jean-Fran├žois Alcover, Apr 01 2018 *)

PROG

(MAGMA) [Floor((Sqrt(2*n-1)-1)/2): n in [1..105]]; // Vincenzo Librandi, Apr 01 2018

CROSSREFS

Sequence in context: A110591 A105209 A179076 * A111855 A071701 A064459

Adjacent sequences:  A095858 A095859 A095860 * A095862 A095863 A095864

KEYWORD

nonn

AUTHOR

Ray Chandler, Jun 20 2004

STATUS

approved

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Last modified March 26 10:18 EDT 2019. Contains 321491 sequences. (Running on oeis4.)