A228208 y-values in the solution to x^2 - 20*y^2 = 176.

1, 2, 5, 7, 14, 19, 37, 50, 97, 131, 254, 343, 665, 898, 1741, 2351, 4558, 6155, 11933, 16114, 31241, 42187, 81790, 110447, 214129, 289154, 560597, 757015, 1467662, 1981891, 3842389, 5188658, 10059505, 13584083, 26336126, 35563591, 68948873, 93106690

Offset: 1

Author

Colin Barker, Aug 16 2013

Keywords

• nonn
• easy

Comments

Also y-values in the solution of x^2-5*y^2=44.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,3,0,-1).

Crossrefs

Cf. A228207, A054486 (bisection).

Programs

Magma

I:=[1,2,5,7,14]; [n le 4 select I[n] else 3*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Aug 17 2013

Mathematica

CoefficientList[Series[(x + 1) (x^2 + x + 1) / ((x^2 - x - 1) (x^2 + x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 17 2013 *)

PARI

Vec(x*(x+1)*(x^2+x+1)/((x^2-x-1)*(x^2+x-1)) + O(x^100))

Formula

G.f.: x*(x+1)*(x^2+x+1) / ((x^2-x-1)*(x^2+x-1)).

a(n) = 3*a(n-2)-a(n-4).

Let h(n) = hypergeom([(1 - n)/2, (n + 1) mod 2 - n/2], [1 - n], -4) then a(n) = h(n-1) + h(n) for n > 2. - Peter Luschny, Sep 03 2019