A105175 Numbers such that 71*(a(n)^2) + 71*a(n) + 1 is a square.

0, 0, 9235919, 14984879, 447402699579360, 725891508817440, 21672901717138141202159, 35163344661747893105039, 1049869992475115099179547651520, 1703368606439836689249786415680, 50857380127742528965284060018658947599, 82513897278978744922944413386362572399

Offset

1,3

Links

Table of n, a(n) for n=1..12.

Index entries for linear recurrences with constant coefficients, signature (1,48441598,-48441598,-1,1).

Formula

Define a(1)=0, a(2)=0, a(3)=9235919, a(4)=14984879. Then a(n) = (a(3)+a(4)+1) * (2*a(n-2)+1) - a(n-3) - 1.

G.f.: -413*x^3*(22363*x^2+13920*x+22363) / ((x-1)*(x^2-6960*x+1)*(x^2+6960*x+1)). - Colin Barker, Apr 17 2014

Mathematica

CoefficientList[Series[-413*x^2*(22363*x^2 + 13920*x + 22363)/((x - 1)*(x^2 - 6960*x + 1)*(x^2 + 6960*x + 1)), {x, 0, 12}], x] (* Wesley Ivan Hurt, Apr 23 2017 *)
LinearRecurrence[{1, 48441598, -48441598, -1, 1}, {0, 0, 9235919, 14984879, 447402699579360}, 20] (* Harvey P. Dale, Nov 20 2022 *)

Prog

(PARI) concat([0, 0], Vec(-413*x^3*(22363*x^2+13920*x+22363) / ((x-1)*(x^2-6960*x+1)*(x^2+6960*x+1)) + O(x^100))) \\ Colin Barker, Apr 17 2014

Crossrefs

Sequence in context: A206599 A245746 A206098 * A212469 A251280 A234395

Adjacent sequences: A105172 A105173 A105174 * A105176 A105177 A105178

Keyword

nonn,easy

Author

Pierre CAMI, Apr 11 2005

Extensions

More terms from Colin Barker, Apr 17 2014

Status

approved