A041273 Denominators of continued fraction convergents to sqrt(149).

1, 4, 5, 29, 92, 305, 1617, 1922, 9305, 225242, 910273, 1135515, 6587848, 20899059, 69285025, 367324184, 436609209, 2113761020, 51166873689, 206781255776, 257948129465, 1496521903101, 4747513838768, 15739063419405, 83442830935793, 99181894355198

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,227164,0,0,0,0,0,0,0,0,1).

Formula

G.f.: -(x^16 -4*x^15 +5*x^14 -29*x^13 +92*x^12 -305*x^11 +1617*x^10 -1922*x^9 +9305*x^8 +1922*x^7 +1617*x^6 +305*x^5 +92*x^4 +29*x^3 +5*x^2 +4*x +1) / ((x^6 +61*x^3 -1)*(x^12 -61*x^9 +3722*x^6 +61*x^3 +1)). - Colin Barker, Nov 14 2013

a(n) = 227164*a(n-9) + a(n-18). - Vincenzo Librandi, Dec 14 2013

Maple

convert(sqrt(149), confrac, 30, cvgts): denom(cvgts); # Wesley Ivan Hurt, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[149], 30]] (* Vincenzo Librandi, Dec 14 2013 *)

Prog

(Magma) I:=[1, 4, 5, 29, 92, 305, 1617, 1922, 9305, 225242, 910273, 1135515, 6587848, 20899059, 69285025, 367324184, 436609209, 2113761020]; [n le 18 select I[n] else 227164*Self(n-9)+Self(n-18): n in [1..40]]; // Vincenzo Librandi, Dec 14 2013

Crossrefs

Cf. A041272, A010202.

Sequence in context: A002352 A042647 A266075 * A256623 A047169 A262034

Adjacent sequences: A041270 A041271 A041272 * A041274 A041275 A041276

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 14 2013

Status

approved