A199774 x-values in the solution to 17*x^2 + 16 = y^2.

0, 3, 5, 32, 203, 333, 2112, 13395, 21973, 139360, 883867, 1449885, 9195648, 58321827, 95670437, 606773408, 3848356715, 6312798957, 40037849280, 253933221363, 416549060725, 2641891279072, 16755744253243, 27485925208893, 174324786569472, 1105625187492675

Offset

1,2

Comments

When are both n-1 and 17*n-1 perfect squares? This problem gives the equation 17*x^2+16=y^2.

Links

Table of n, a(n) for n=1..26.

Index entries for linear recurrences with constant coefficients, signature (0,0,66,0,0,-1).

Formula

a(n) = 66*a(n-3) - a(n-6), a(1)=0, a(2)=3, a(3)=5, a(4)=32, a(5)=203, a(6)=333.

G.f.: x^2*(3*x^4+5*x^3+32*x^2+5*x+3) / (x^6-66*x^3+1). - Colin Barker, Sep 01 2013

Example

a(7)=66*32-0=2112.

Mathematica

LinearRecurrence[{0, 0, 66, 0, 0, -1}, {0, 3, 5, 32, 203, 333}, 50]

Prog

(PARI) Vec(x^2*(3*x^4+5*x^3+32*x^2+5*x+3)/(x^6-66*x^3+1) + O(x^100)) \\ Colin Barker, Sep 01 2013

Crossrefs

Cf. A199772, A199773, A199798.

Sequence in context: A109173 A179387 A295364 * A235267 A284379 A103010

Adjacent sequences: A199771 A199772 A199773 * A199775 A199776 A199777

Keyword

nonn,easy

Author

Sture Sjöstedt, Nov 10 2011

Extensions

More terms from T. D. Noe, Nov 10 2011

Status

approved