OFFSET
0,1
COMMENTS
a(n) gives the values of y satifacting 3*x^2 - y^2 = 507; corresponding x values are given by A293817.
a(n)/3 is the radius of the inscribed circle.
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).
FORMULA
a(n) = 4*a(n-3) - a(n-6), a(1)=9, a(2)=24, a(3)=39, a(4)=60, a(5)=105, a(6)=156.
G.f.: 3*(3 + 8*x + 13*x^2 + 8*x^3 + 3*x^4) / (1 - 4*x^3 + x^6). - Colin Barker, Dec 27 2017
EXAMPLE
If the sides are 15, 28, 41 the triangle has the altitude 9 and is a part of the Pythagorean triangle with the sides 9, 40, 41, so 9 is a term.
MATHEMATICA
CoefficientList[ Series[ 3(3x^4 +8x^3 +13x^2 +8x +3)/(x^6 -4x^3 +1), {x, 0, 35}], x] (* or *)
LinearRecurrence[{0, 0, 4, 0, 0, -1}, 3 {3, 8, 13, 20, 35, 52}, 36] (* Robert G. Wilson v, Dec 27 2017 *)
PROG
(PARI) Vec(3*(3 + 8*x + 13*x^2 + 8*x^3 + 3*x^4) / (1 - 4*x^3 + x^6) + O(x^40)) \\ Colin Barker, Dec 27 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Sture Sjöstedt, Dec 27 2017
STATUS
approved