A296795 Numbers k such that m = 2*k is the middle side in a Heronian triangle with sides m - 11, m, m + 11.

13, 14, 22, 38, 43, 77, 139, 158, 286, 518, 589, 1067, 1933, 2198, 3982, 7214, 8203, 14861, 26923, 30614, 55462, 100478, 114253, 206987, 374989, 426398, 772486, 1399478, 1591339, 2882957, 5222923, 5938958, 10759342, 19492214, 22164493, 40154411, 72745933

Offset

0,1

Comments

a(n) gives values of x satisfying 3*x^2 - y^2 = 363; the corresponding y values are given by A296796.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Wikipedia, Heronian triangle

Index entries for linear recurrences with constant coefficients, signature (0,0,4,0,0,-1).

Formula

From Colin Barker, Dec 22 2017: (Start)

G.f.: (13 + 14*x + 22*x^2 - 14*x^3 - 13*x^4 - 11*x^5) / (1 - 4*x^3 + x^6).

a(n) = 4*a(n-3) - a(n-6) for n>5.

(End)

Example

The smallest triangle of this type has following sides: 15, 26, 37 has the altitude 12 and is a part of the Pythagorean triangle with sides : 12, 35, 37.

Mathematica

CoefficientList[Series[(13 + 14 x + 22 x^2 - 14 x^3 - 13 x^4 - 11 x^5)/(1 - 4 x^3 + x^6), {x, 0, 36}], x] (* Michael De Vlieger, Dec 22 2017 *)

Prog

(PARI) Vec((13 + 14*x + 22*x^2 - 14*x^3 - 13*x^4 - 11*x^5) / (1 - 4*x^3 + x^6) + O(x^40)) \\ Colin Barker, Dec 22 2017

Crossrefs

Cf. A003500, A005320, A296796.

Sequence in context: A360258 A360528 A336004 * A079831 A022803 A112653

Adjacent sequences: A296792 A296793 A296794 * A296796 A296797 A296798

Keyword

nonn,easy

Author

Sture Sjöstedt, Dec 20 2017

Extensions

More terms from Colin Barker, Dec 22 2017

Status

approved