A041072 Numerators of continued fraction convergents to sqrt(43).

6, 7, 13, 46, 59, 341, 400, 1541, 1941, 3482, 43725, 47207, 90932, 320003, 410935, 2374678, 2785613, 10731517, 13517130, 24248647, 304500894, 328749541, 633250435, 2228500846, 2861751281, 16537257251

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Les Tablettes du Chercheur, Problem 364, pp. 11, Mai 15 1891
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,6964,0,0,0,0,0,0,0,0,0,-1).

Crossrefs

Cf. A041073, A010497, A010134.

Programs

Mathematica

Numerator[Convergents[Sqrt[43], 30]] (* Vincenzo Librandi, Oct 29 2013 *)

Formula

G.f.: -(x^19 -6*x^18 +7*x^17 -13*x^16 +46*x^15 -59*x^14 +341*x^13 -400*x^12 +1541*x^11 -1941*x^10 -3482*x^9 -1941*x^8 -1541*x^7 -400*x^6 -341*x^5 -59*x^4 -46*x^3 -13*x^2 -7*x -6) / (x^20 -6964*x^10 +1). - Colin Barker, Nov 04 2013