A386201 Lengths of the long leg in the unique primitive Pythagorean triple whose inradius is A000032(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

12, 4, 24, 40, 112, 264, 684, 1740, 4512, 11704, 30504, 79600, 208012, 543924, 1422984, 3723720, 9746112, 25511224, 66782124, 174826300, 457682512, 1198198104, 3136874424, 8212364640, 21500121612, 56287841764, 147363147384, 385801185640, 1010039738512

Offset

0,1

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,1,-5,-1,1).

Formula

a(n) = 2 * A000032(n) * (A000032(n) + 1).

G.f.: 4*(3 - 8*x + 6*x^3)/((1 + x)*(1 - 3*x + x^2)*(1 - x - x^2)). - Andrew Howroyd, Nov 12 2025

Mathematica

A386201[n_] := 2*#*(# + 1) & [LucasL[n]]; Array[A386201, 30, 0] (* or *)
LinearRecurrence[{3, 1, -5, -1, 1}, {12, 4, 24, 40, 112}, 30] (* Paolo Xausa, Jan 03 2026 *)

Prog

(PARI) a(n) = my(t=fibonacci(n+1) + fibonacci(n-1)); 2*t*(t + 1) \\ Andrew Howroyd, Nov 12 2025

Crossrefs

Cf. A000032, A380821 (short legs).

Sequence in context: A199693 A166206 A040137 * A092237 A367323 A081987

Adjacent sequences: A386198 A386199 A386200 * A386202 A386203 A386204

Keyword

nonn,easy

Author

Miguel-Ángel Pérez García-Ortega, Jul 14 2025

Status

approved