A041652 Numerators of continued fraction convergents to sqrt(345).

18, 19, 37, 93, 130, 873, 1003, 2879, 3882, 6761, 247278, 254039, 501317, 1256673, 1757990, 11804613, 13562603, 38929819, 52492422, 91422241, 3343693098, 3435115339, 6778808437, 16992732213, 23771540650, 159621976113, 183393516763, 526409009639, 709802526402

Offset

0,1

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, 13522, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^19 -18*x^18 +19*x^17 -37*x^16 +93*x^15 -130*x^14 +873*x^13 -1003*x^12 +2879*x^11 -3882*x^10 -6761*x^9 -3882*x^8 -2879*x^7 -1003*x^6 -873*x^5 -130*x^4 -93*x^3 -37*x^2 -19*x -18) / (x^20 -13522*x^10 +1). - Colin Barker, Nov 10 2013

Mathematica

Numerator[Convergents[Sqrt[345], 30]] (* Vincenzo Librandi, Nov 06 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 13522, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {18, 19, 37, 93, 130, 873, 1003, 2879, 3882, 6761, 247278, 254039, 501317, 1256673, 1757990, 11804613, 13562603, 38929819, 52492422, 91422241}, 30] (* Harvey P. Dale, Feb 18 2023 *)

Crossrefs

Cf. A041653.

Sequence in context: A041656 A042507 A041658 * A041650 A041648 A034122

Adjacent sequences: A041649 A041650 A041651 * A041653 A041654 A041655

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 10 2013

Status

approved