A041507 Denominators of continued fraction convergents to sqrt(270).

1, 2, 7, 44, 139, 322, 10443, 21208, 74067, 465610, 1470897, 3407404, 110507825, 224423054, 783776987, 4927084976, 15565031915, 36057148806, 1169393793707, 2374844736220, 8293928002367, 52138412750422, 164709166253633, 381556745257688

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,10582,0,0,0,0,0,-1).

Formula

G.f.: -(x^10 -2*x^9 +7*x^8 -44*x^7 +139*x^6 -322*x^5 -139*x^4 -44*x^3 -7*x^2 -2*x -1) / ((x^4 -22*x^2 +1)*(x^8 +22*x^6 +483*x^4 +22*x^2 +1)). - Colin Barker, Nov 18 2013

a(n) = 10582*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 19 2013

Mathematica

Denominator[Convergents[Sqrt[270], 30]] (* Vincenzo Librandi, Dec 19 2013 *)

Prog

(Magma) I:=[1, 2, 7, 44, 139, 322, 10443, 21208, 74067, 465610, 1470897, 3407404]; [n le 12 select I[n] else 10582*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Dec 19 2013

Crossrefs

Cf. A041506, A040253.

Sequence in context: A270348 A270580 A103084 * A158107 A145073 A111561

Adjacent sequences: A041504 A041505 A041506 * A041508 A041509 A041510

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved