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A101903
Number of twin Pythagorean triples with hypotenuse less than 10^n.
0
1, 7, 24, 74, 228, 712, 2243, 7079, 22370, 70722, 223619, 707120, 2236083, 7071084, 22360697, 70710696, 223606818, 707106802, 2236067999, 7071067836, 22360679800, 70710678145, 223606797778, 707106781216, 2236067977530
OFFSET
1,2
COMMENTS
a(n) <= 10^(n/2)/sqrt(2). - Robert G. Wilson v, Jan 08 2005
LINKS
Ravi P. Agarwal, Pythagorean Triples Before and after Pythagoras, Computation 2020, 8(3), 62, p. 14.
Eric Weisstein's World of Mathematics, Twin Pythagorean Triple
EXAMPLE
For a(2)=7 because {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {20, 21, 29}, {9, 40, 41}, {11, 60, 61}, {13, 84, 85}.
MATHEMATICA
f[n_] := Round[ Sqrt[ (10^n - 1)/2] - 1]; a[n_] := (MatrixPower[{{1, 2, 2}, {2, 1, 2}, {2, 2, 3}}, n].{{1}, {0}, {1}})[[3, 1]]; t = Table[ a[n], {n, 2, 35}]; g[n_] := Length[ Select[t, # < 10^n &]]; Table[f[n] + g[n], {n, 25}] (* Robert G. Wilson v, Jan 08 2005 *)
CROSSREFS
Sequence in context: A211381 A339254 A305676 * A212504 A196349 A196352
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Dec 20 2004
EXTENSIONS
a(5) and up from Robert G. Wilson v, Jan 08 2005
STATUS
approved