A041699 Denominators of continued fraction convergents to sqrt(369).

1, 4, 5, 19, 43, 320, 1323, 9581, 20485, 71036, 91521, 437120, 16702081, 67245444, 83947525, 319088019, 722123563, 5373952960, 22217935403, 160899500781, 344016936965, 1192950311676, 1536967248641, 7340819306240, 280488100885761, 1129293222849284

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, 16793602, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: (1 +4*x +5*x^2 +19*x^3 +43*x^4 +320*x^5 +1323*x^6 +9581*x^7 +20485*x^8 +71036*x^9 +91521*x^10 +437120*x^11 -91521*x^12 +71036*x^13 -20485*x^14 +9581*x^15 -1323*x^16 +320*x^17 -43*x^18 +19*x^19 -5*x^20 +4*x^21 -x^22)/(1 -16793602*x^12 +x^24). - Vincenzo Librandi, Dec 23 2013

a(n) = 16793602*a(n-12) - a(n-24) for n>23. - Vincenzo Librandi, Dec 23 2013

Mathematica

Denominator[Convergents[Sqrt[369], 30]] (* or *) CoefficientList[Series[(1 + 4 x + 5 x^2 + 19 x^3 + 43 x^4 + 320 x^5 + 1323 x^6 + 9581 x^7 + 20485 x^8 + 71036 x^9 + 91521 x^10 + 437120 x^11 - 91521 x^12 + 71036 x^13 - 20485 x^14 + 9581 x^15 - 1323 x^16 + 320 x^17 - 43 x^18 + 19 x^19 - 5 x^20 + 4 x^21 - x^22)/(1 - 16793602 x^12 + x^24), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 23 2013 *)

Crossrefs

Cf. A041698.

Sequence in context: A042085 A136211 A041036 * A154704 A047023 A032319

Adjacent sequences: A041696 A041697 A041698 * A041700 A041701 A041702

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Dec 23 2013

Status

approved