A042722 Numerators of continued fraction convergents to sqrt(891).

29, 30, 179, 209, 388, 597, 3373, 3970, 233633, 237603, 1421648, 1659251, 3080899, 4740150, 26781649, 31521799, 1855045991, 1886567790, 11287884941, 13174452731, 24462337672, 37636790403, 212646289687

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, 7940, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: (29 +30*x +179*x^2 +209*x^3 +388*x^4 +597*x^5 +3373*x^6 +3970*x^7 +3373*x^8 -597*x^9 +388*x^10 -209*x^11 +179*x^12 -30*x^13 +29*x^14 -x^15)/(1 -7940*x^8 +x^16). - Vincenzo Librandi, Dec 02 2013

a(n) = 7940*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 02 2013

Mathematica

Numerator[Convergents[Sqrt[891], 30]]
(* or *)
CoefficientList[Series[(29 + 30 x + 179 x^2 + 209 x^3 + 388 x^4 + 597 x^5 + 3373 x^6 + 3970 x^7 + 3373 x^8 - 597 x^9 + 388 x^10 - 209 x^11 + 179 x^12 - 30 x^13 + 29 x^14 - x^15)/(1-7940 x^8 + x^16), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 02 2013 *)

Prog

(Magma) I:=[29, 30, 179, 209, 388, 597, 3373, 3970, 233633, 237603, 1421648, 1659251, 3080899, 4740150, 26781649, 31521799]; [n le 16 select I[n] else 7940*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Dec 02 2013

Crossrefs

Cf. A042723.

Sequence in context: A042712 A042720 A042718 * A042724 A042726 A042728

Adjacent sequences: A042719 A042720 A042721 * A042723 A042724 A042725

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved