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
KEYWORD
nonn,easy
AUTHOR
Sture Sjöstedt, Dec 20 2017
EXTENSIONS
More terms from Colin Barker, Dec 22 2017
STATUS
approved