A199336 x-values in the solution to 15*x^2 - 14 = y^2.

1, 3, 5, 23, 39, 181, 307, 1425, 2417, 11219, 19029, 88327, 149815, 695397, 1179491, 5474849, 9286113, 43103395, 73109413, 339352311, 575589191, 2671715093, 4531604115, 21034368433, 35677243729, 165603232371, 280886345717, 1303791490535, 2211413522007

Offset: 1

Author

Sture Sjöstedt, Nov 05 2011

Keywords

• nonn
• easy

Comments

When are both n+1 and 15*n+1 perfect squares? This problem gives the equation 15*x^2-14 = y^2.

Values of x (or y) in the solutions to x^2 - 8xy + y^2 + 14 = 0. - Colin Barker, Feb 05 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..250
• Index entries for linear recurrences with constant coefficients, signature (0,8,0,-1).

Crossrefs

Cf. A198947, A199338.

Essentially the second differences of A237262. Cf. also A322780.

Programs

Magma

m:=29; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x)*(1+4*x+x^2)/(1-8*x^2+x^4))); // Bruno Berselli, Nov 08 2011

Mathematica

LinearRecurrence[{0, 8, 0, -1}, {1, 3, 5, 23}, 50] (* T. D. Noe, Nov 07 2011 *)

Formula

a(n+4) = 8*a(n+2) - a(n), a(1)=1, a(2)=3, a(3)=5, a(4)=23.

G.f.: x*(1-x)*(1+4*x+x^2)/(1-8*x^2+x^4). - Bruno Berselli, Nov 08 2011

Extensions

More terms from T. D. Noe, Nov 07 2011