A199338 y-values in the solution to 15*x^2 - 14 = y^2.

1, 11, 19, 89, 151, 701, 1189, 5519, 9361, 43451, 73699, 342089, 580231, 2693261, 4568149, 21203999, 35964961, 166938731, 283151539, 1314305849, 2229247351, 10347508061, 17550827269, 81465758639, 138177370801, 641378561051, 1087868139139, 5049562729769

Offset: 1

Author

Sture Sjöstedt, Nov 08 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.

Essentially the same as A103201. - R. J. Mathar, Nov 11 2011

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (0,8,0,-1).

Crossrefs

Cf. A199336.

Programs

Magma

m:=29; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1+x)*(1+10*x+x^2)/(1-8*x^2+x^4))); // Bruno Berselli, Nov 08 2011

Mathematica

LinearRecurrence[{0, 8, 0, -1}, {1, 11, 19, 89}, 50]

Formula

a(n+4) = 8*a(n+2) - a(n) with a(1)=1, a(2)=11, a(3)=19, a(4)=89.

G.f.: x*(1+x)*(1+10*x+x^2)/(1-8*x^2+x^4). - Bruno Berselli, Nov 08 2011