A042360 Numerators of continued fraction convergents to sqrt(707).

26, 27, 53, 133, 452, 1037, 1489, 2526, 132841, 135367, 268208, 671783, 2283557, 5238897, 7522454, 12761351, 671112706, 683874057, 1354986763, 3393847583, 11536529512, 26466906607, 38003436119, 64470342726

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, 5052, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: (26 +27*x +53*x^2 +133*x^3 +452*x^4 +1037*x^5 +1489*x^6 +2526*x^7 +1489*x^8 -1037*x^9 +452*x^10 -133*x^11 +53*x^12 -27*x^13 +26*x^14 -x^15)/(1 -5052*x^8 +x^16). - Vincenzo Librandi, Nov 22 2013

a(n) = 5052*a(n-8) - a(n-16). - Vincenzo Librandi, Nov 22 2013

Mathematica

Numerator[Convergents[Sqrt[707], 30]] (* or *) CoefficientList[Series[(26 + 27 x + 53 x^2 + 133 x^3 + 452 x^4 + 1037 x^5 + 1489 x^6 + 2526 x^7 + 1489 x^8 - 1037 x^9 + 452 x^10 - 133 x^11 + 53 x^12 - 27 x^13 + 26 x^14 - x^15)/(1 - 5052 x^8 + x^16), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 22 2013 *)

Prog

(Magma) I:=[26, 27, 53, 133, 452, 1037, 1489, 2526, 132841, 135367, 268208, 671783, 2283557, 5238897, 7522454, 12761351]; [n le 16 select I[n] else 5052*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Nov 22 2013

Crossrefs

Cf. A042361.

Sequence in context: A042364 A042366 A042368 * A042358 A042356 A042354

Adjacent sequences: A042357 A042358 A042359 * A042361 A042362 A042363

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved