A293817 Numbers k such that m=2*k is the middle side in a Heronian triangle with sides m-13, m , m+13.

13, 14, 19, 26, 37, 62, 91, 134, 229, 338, 499, 854, 1261, 1862, 3187, 4706, 6949, 11894, 17563, 25934, 44389, 65546, 96787, 165662, 244621, 361214, 618259, 912938, 1348069, 2307374, 3407131, 5031062, 8611237, 12715586, 18776179, 32137574, 47455213, 70073654

Offset: 0

Author

Sture Sjöstedt, Dec 27 2017

Keywords

• nonn
• easy

Comments

a(n) gives values of x satisfying 3*x^2 - y^2 = 507; corresponding y values are given by A293846.

Examples

			The smallest triangle of this type with 3 acute angles has the sides: 61, 74, 87.
		

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,4,0,0,-1).

Crossrefs

Cf. A003500, A005320, A296795, A296796.

Programs

Mathematica

LinearRecurrence[{0,0,4,0,0,-1},{13,14,19,26,37,62},40] (* Harvey P. Dale, Oct 10 2023 *)

PARI

Vec((13 + 14*x + 19*x^2 - 26*x^3 - 19*x^4 - 14*x^5) / (1 - 4*x^3 + x^6) + O(x^40)) \\ Colin Barker, Dec 27 2017

Formula

a(n) = 4*a(n-3)-a(n-6), a(1)= 13, a(2)= 14, a(3)= 19, a(4)= 26, a(5)= 37, a(6)= 62.

G.f.: (13 + 14*x + 19*x^2 - 26*x^3 - 19*x^4 - 14*x^5) / (1 - 4*x^3 + x^6). - Colin Barker, Dec 27 2017