A042400 Numerators of continued fraction convergents to sqrt(727).

26, 27, 701, 728, 38557, 39285, 1020682, 1059967, 56138966, 57198933, 1486112291, 1543311224, 81738295939, 83281607163, 2163778475014, 2247060082177, 119010902748218, 121257962830395, 3150459973508093

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, 1456, 0, 0, 0, -1).

Formula

G.f.: (26 +27*x +701*x^2 +728*x^3 +701*x^4 -27*x^5 +26*x^6 -x^7)/(1 -1456*x^4 +x^8). - Vincenzo Librandi, Nov 23 2013

a(n) = 1456*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 23 2013

Mathematica

Numerator[Convergents[Sqrt[727], 30]] (* or *) CoefficientList[Series[(26 + 27 x + 701 x^2 + 728 x^3 + 701 x^4 - 27 x^5 + 26 x^6 - x^7)/(1 - 1456 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 23 2013 *)

Prog

(Magma) I:=[26, 27, 701, 728, 38557, 39285, 1020682, 1059967]; [n le 8 select I[n] else 1456*Self(n-4)-Self(n-8): n in [1..30]]; //  Vincenzo Librandi, Nov 23 2013

Crossrefs

Cf. A042401.

Sequence in context: A137119 A042396 A042398 * A042401 A042402 A247394

Adjacent sequences: A042397 A042398 A042399 * A042401 A042402 A042403

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved