A041887 Denominators of continued fraction convergents to sqrt(465).

1, 1, 2, 7, 16, 39, 94, 321, 415, 736, 31327, 32063, 63390, 222233, 507856, 1237945, 2983746, 10189183, 13172929, 23362112, 994381633, 1017743745, 2012125378, 7054119879, 16120365136, 39294850151, 94710065438, 323425046465, 418135111903, 741560158368

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,31742,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^18 -x^17 +2*x^16 -7*x^15 +16*x^14 -39*x^13 +94*x^12 -321*x^11 +415*x^10 -736*x^9 -415*x^8 -321*x^7 -94*x^6 -39*x^5 -16*x^4 -7*x^3 -2*x^2 -x -1) / (x^20 -31742*x^10 +1). - Colin Barker, Nov 26 2013

a(n) = 31742*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 26 2013

Mathematica

Denominator[Convergents[Sqrt[465], 30]] (* Vincenzo Librandi, Dec 26 2013 *)

Prog

(Magma) I:=[1, 1, 2, 7, 16, 39, 94, 321, 415, 736, 31327, 32063, 63390, 222233, 507856, 1237945, 2983746, 10189183, 13172929, 23362112]; [n le 20 select I[n] else 31742*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 26 2013

Crossrefs

Cf. A041886, A040443.

Sequence in context: A260505 A042243 A293378 * A129441 A093971 A065497

Adjacent sequences: A041884 A041885 A041886 * A041888 A041889 A041890

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 26 2013

Status

approved