A041573 Denominators of continued fraction convergents to sqrt(304).

1, 2, 7, 16, 23, 39, 62, 101, 163, 427, 1444, 3315, 114154, 231623, 809023, 1849669, 2658692, 4508361, 7167053, 11675414, 18842467, 49360348, 166923511, 383207370, 13195974091, 26775155552, 93521440747, 213818037046, 307339477793, 521157514839

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,115598,0,0,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^22 -2*x^21 +7*x^20 -16*x^19 +23*x^18 -39*x^17 +62*x^16 -101*x^15 +163*x^14 -427*x^13 +1444*x^12 -3315*x^11 -1444*x^10 -427*x^9 -163*x^8 -101*x^7 -62*x^6 -39*x^5 -23*x^4 -16*x^3 -7*x^2 -2*x -1) / ((x^12 -340*x^6 +1)*(x^12 +340*x^6 +1)). - Colin Barker, Nov 19 2013

a(n) = 115598*a(n-12) - a(n-24) for n>23. - Vincenzo Librandi, Dec 20 2013

Mathematica

Denominator[Convergents[Sqrt[304], 30]] (* Vincenzo Librandi, Dec 20 2013 *)

Prog

(Magma) I:=[1, 2, 7, 16, 23, 39, 62, 101, 163, 427, 1444, 3315, 114154, 231623, 809023, 1849669, 2658692, 4508361, 7167053, 11675414, 18842467, 49360348, 166923511, 383207370]; [n le 24 select I[n] else 115598*Self(n-12)-Self(n-24): n in [1..40]]; // Vincenzo Librandi, Dec 20 2013

Crossrefs

Cf. A041572, A040286.

Sequence in context: A233580 A225323 A167236 * A211053 A041341 A296857

Adjacent sequences: A041570 A041571 A041572 * A041574 A041575 A041576

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 19 2013

Status

approved