A041805 Denominators of continued fraction convergents to sqrt(423).

1, 1, 2, 7, 30, 97, 127, 224, 9087, 9311, 18398, 64505, 276418, 893759, 1170177, 2063936, 83727617, 85791553, 169519170, 594349063, 2546915422, 8235095329, 10782010751, 19017106080, 771466253951, 790483360031, 1561949613982, 5476332201977, 23467278421890

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

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, 9214, 0, 0, 0, 0, 0, 0, 0, -1).

Crossrefs

Cf. A041804, A040402.

Programs

Magma

I:=[1,1,2,7,30,97,127,224,9087,9311,18398,64505, 276418,893759,1170177,2063936]; [n le 16 select I[n] else 9214*Self(n-8)-Self(n-16): n in [1..50]]; // Vincenzo Librandi, Dec 24 2013

Mathematica

Denominator[Convergents[Sqrt[423], 30]] (* Vincenzo Librandi, Dec 24 2013 *)

Formula

G.f.: -(x^14 -x^13 +2*x^12 -7*x^11 +30*x^10 -97*x^9 +127*x^8 -224*x^7 -127*x^6 -97*x^5 -30*x^4 -7*x^3 -2*x^2 -x -1) / ((x^8 -96*x^4 +1)*(x^8 +96*x^4 +1)). - Colin Barker, Nov 25 2013

a(n) = 9214*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 24 2013

Extensions

More terms from Colin Barker, Nov 25 2013