A041447 Denominators of continued fraction convergents to sqrt(239).

1, 2, 11, 13, 37, 161, 2452, 9969, 22390, 32359, 184185, 400729, 12206055, 24812839, 136270250, 161083089, 458436428, 1994828801, 30380868443, 123518302573, 277417473589, 400935776162, 2282096354399, 4965128484960, 151235950903199, 307437030291358

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,12390240,0,0,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: (1 +2*x +11*x^2 +13*x^3 +37*x^4 +161*x^5 +2452*x^6 +9969*x^7 +22390*x^8 +32359*x^9 +184185*x^10 +400729*x^11 -184185*x^12 +32359*x^13 -22390*x^14 +9969*x^15 -2452*x^16 +161*x^17 -37*x^18 +13*x^19 -11*x^20 +2*x^21 -x^22)/(1 -12390240*x^12 +x^24). - Vincenzo Librandi, Dec 18 2013

a(n) = 12390240*a(n-12) - a(n-24) for n>23. - Vincenzo Librandi, Dec 18 2013

Mathematica

Denominator[Convergents[Sqrt[239], 30]] (* or *) CoefficientList[Series[(1 +2 x + 11 x^2 + 13 x^3 + 37 x^4 + 161 x^5 + 2452 x^6 + 9969 x^7 + 22390 x^8 + 32359 x^9 + 184185 x^10 + 400729 x^11 - 184185 x^12 + 32359 x^13 - 22390 x^14 + 9969 x^15 - 2452 x^16 + 161 x^17 - 37 x^18 + 13 x^19 - 11 x^20 + 2 x^21 - x^22)/(1 - 12390240 x^12 + x^24), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 18 2013 *)

Prog

(Magma) I:=[1, 2, 11, 13, 37, 161, 2452, 9969, 22390, 32359, 184185, 400729, 12206055, 24812839, 136270250, 161083089, 458436428, 1994828801, 30380868443, 123518302573, 277417473589, 400935776162, 2282096354399, 4965128484960]; [n le 24 select I[n] else 12390240*Self(n-12)-Self(n-24): n in [1..30]]; // Vincenzo Librandi, Dec 18 2013

Crossrefs

Cf. A041446.

Sequence in context: A023288 A106960 A084405 * A291464 A262832 A091021

Adjacent sequences: A041444 A041445 A041446 * A041448 A041449 A041450

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 18 2013

Status

approved