A041895 Denominators of continued fraction convergents to sqrt(469).

1, 1, 2, 3, 32, 195, 1982, 2177, 4159, 6336, 270271, 276607, 546878, 823485, 8781728, 53513853, 543920258, 597434111, 1141354369, 1738788480, 74170470529, 75909259009, 150079729538, 225988988547, 2409969615008, 14685806678595, 149268036400958

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, 274430, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^18 -x^17 +2*x^16 -3*x^15 +32*x^14 -195*x^13 +1982*x^12 -2177*x^11 +4159*x^10 -6336*x^9 -4159*x^8 -2177*x^7 -1982*x^6 -195*x^5 -32*x^4 -3*x^3 -2*x^2 -x -1) / (x^20 -274430*x^10 +1). - Colin Barker, Nov 26 2013

a(n) = 274430*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 26 2013

Mathematica

Denominator[Convergents[Sqrt[469], 30]] (* Vincenzo Librandi, Dec 26 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 274430, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 1, 2, 3, 32, 195, 1982, 2177, 4159, 6336, 270271, 276607, 546878, 823485, 8781728, 53513853, 543920258, 597434111, 1141354369, 1738788480}, 30] (* Harvey P. Dale, Mar 23 2023 *)

Prog

(Magma) I:=[1, 1, 2, 3, 32, 195, 1982, 2177, 4159, 6336, 270271, 276607, 546878, 823485, 8781728, 53513853, 543920258, 597434111, 1141354369, 1738788480]; [n le 20 select I[n] else 274430*Self(n-10)-Self(n-20): n in [1..50]]; // Vincenzo Librandi, Dec 26 2013

Crossrefs

Cf. A041894, A176443, A040447.

Sequence in context: A052830 A357265 A356904 * A371117 A277481 A079883

Adjacent sequences: A041892 A041893 A041894 * A041896 A041897 A041898

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 26 2013

Status

approved