A377725 Length of the short leg of the unique primitive Pythagorean triple whose inradius is A002315(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

3, 15, 83, 479, 2787, 16239, 94643, 551615, 3215043, 18738639, 109216787, 636562079, 3710155683, 21624372015, 126036076403, 734592086399, 4281516441987, 24954506565519, 145445522951123, 847718631141215, 4940866263896163, 28797478952235759, 167844007449518387

Offset

0,1

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

Miguel-Ángel Pérez García-Ortega, Capitulo 5. Catetos, El Libro de las Ternas Pitagóricas.

Index entries for linear recurrences with constant coefficients, signature (7,-7,1).

Formula

a(n) = 2*A002315(n) + 1.

G.f.: (3 - 6*x - x^2)/((1 - x)*(1 - 6*x + x^2)). - Andrew Howroyd, Nov 16 2025

Example

Triangles begin:
  n=0:      3,         4,         5;
  n=1:     15,       112,       113;
  n=2:     83,      3444,      3445;
  n=3:    479,    114720,    114721;
  ...
This sequence gives the first column.

Mathematica

LinearRecurrence[{7, -7, 1}, {3, 15, 83}, 25] (* Paolo Xausa, Jan 09 2026 *)

Prog

(PARI) a(n)=my(t=polcoef((1 + x)/(1 - 6*x + x^2) + O(x*x^n), n)); 2*t + 1; \\ Andrew Howroyd, Nov 16 2025

Crossrefs

Cf. A002315, A377016, A377726, A378380 (semiperimeter), A378386 (area), A379509 (sum of legs), A385977 (long leg).

Sequence in context: A192662 A213096 A052451 * A026019 A354660 A118356

Adjacent sequences: A377722 A377723 A377724 * A377726 A377727 A377728

Keyword

nonn,easy

Author

Miguel-Ángel Pérez García-Ortega, Nov 05 2024

Extensions

Offset corrected by Andrew Howroyd, Nov 16 2025

Status

approved