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A041573 Denominators of continued fraction convergents to sqrt(304). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 18 16:00 EDT 2019. Contains 321292 sequences. (Running on oeis4.)