A041907 Denominators of continued fraction convergents to sqrt(475).

1, 1, 4, 5, 34, 73, 472, 545, 2107, 2652, 113491, 116143, 461920, 578063, 3930298, 8438659, 54562252, 63000911, 243564985, 306565896, 13119332617, 13425898513, 53397028156, 66822926669, 454334588170, 975492103009, 6307287206224, 7282779309233

Offset

0,3

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, 115598, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^18 -x^17 +4*x^16 -5*x^15 +34*x^14 -73*x^13 +472*x^12 -545*x^11 +2107*x^10 -2652*x^9 -2107*x^8 -545*x^7 -472*x^6 -73*x^5 -34*x^4 -5*x^3 -4*x^2 -x -1) / ((x^10 -340*x^5 +1)*(x^10 +340*x^5 +1)). - Colin Barker, Nov 27 2013

a(n) = 115598*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 27 2013

Mathematica

Denominator[Convergents[Sqrt[475], 30]] (* Vincenzo Librandi, Dec 27 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 115598, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 1, 4, 5, 34, 73, 472, 545, 2107, 2652, 113491, 116143, 461920, 578063, 3930298, 8438659, 54562252, 63000911, 243564985, 306565896}, 30] (* Harvey P. Dale, Jul 08 2020 *)

Prog

(Magma) I:=[1, 1, 4, 5, 34, 73, 472, 545, 2107, 2652, 113491, 116143, 461920, 578063, 3930298, 8438659, 54562252, 63000911, 243564985, 306565896]; [n le 20 select I[n] else 115598*Self(n-10)-Self(n-20): n in [1..50]]; // Vincenzo Librandi, Dec 27 2013

Crossrefs

Cf. A041906, A040453.

Sequence in context: A376536 A378079 A244333 * A228662 A151450 A243772

Adjacent sequences: A041904 A041905 A041906 * A041908 A041909 A041910

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 27 2013

Status

approved