A042370 Numerators of continued fraction convergents to sqrt(712).

26, 27, 80, 507, 1094, 1601, 84346, 85947, 256240, 1623387, 3503014, 5126401, 270075866, 275202267, 820480400, 5198084667, 11216649734, 16414734401, 864782838586, 881197572987, 2627177984560, 16644265480347

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,3202,0,0,0,0,0,-1).

Formula

G.f.: (26 + 27*x + 80*x^2 + 507*x^3 + 1094*x^4 + 1601*x^5 + 1094*x^6 - 507*x^7 + 80*x^8 - 27*x^9 + 26*x^10 - x^11)/(1 - 3202*x^6 + x^12). - Vincenzo Librandi, Nov 22 2013

a(n) = 3202*a(n-6) - a(n-12). - Vincenzo Librandi, Nov 22 2013

Mathematica

Numerator[Convergents[Sqrt[712], 30]] (* or *) CoefficientList[Series[(26 + 27 x + 80 x^2 + 507 x^3 + 1094 x^4 + 1601 x^5 + 1094 x^6 - 507 x^7 + 80 x^8 - 27 x^9 + 26 x^10 - x^11)/(1 - 3202 x^6 + x^12), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 22 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 3202, 0, 0, 0, 0, 0, -1}, {26, 27, 80, 507, 1094, 1601, 84346, 85947, 256240, 1623387, 3503014, 5126401}, 40] (* Harvey P. Dale, Jul 08 2018 *)

Prog

(Magma) I:=[26, 27, 80, 507, 1094, 1601, 84346, 85947, 256240, 1623387, 3503014, 5126401]; [n le 12 select I[n] else 3202*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 22 2013

Crossrefs

Cf. A042371.

Sequence in context: A042374 A042376 A042372 * A042382 A042380 A042378

Adjacent sequences: A042367 A042368 A042369 * A042371 A042372 A042373

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved