A041621 Denominators of continued fraction convergents to sqrt(329).

1, 7, 29, 65, 94, 159, 730, 889, 1619, 4127, 18127, 131016, 4734703, 33273937, 137830451, 308934839, 446765290, 755700129, 3469565806, 4225265935, 7694831741, 19614929417, 86154549409, 622696775280, 22503238459489, 158145365991703, 655084702426301

Offset

0,2

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, 0, 0, 0, 0, 4752830, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f. (1 +7*x +29*x^2 +65*x^3 +94*x^4 +159*x^5 +730*x^6 +889*x^7 +1619*x^8 +4127*x^9 +18127*x^10 +131016*x^11 -18127*x^12 +4127*x^13 -1619*x^14 +889*x^15 -730*x^16 +159*x^17 -94*x^18 +65*x^19 -29*x^20 +7*x^21 -x^22)/(1 -4752830*x^12 +x^24). - Vincenzo Librandi, Dec 22 2013

a(n) = 4752830*a(n-12) - a(n-24) for n>23. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[329], 30]] (* or *) CoefficientList[Series[(1 + 7 x + 29 x^2 + 65 x^3 + 94 x^4 + 159 x^5 + 730 x^6 + 889 x^7 + 1619 x^8 + 4127 x^9 + 18127 x^10 + 131016 x^11 - 18127 x^12 + 4127 x^13 - 1619 x^14 + 889 x^15 - 730 x^16 + 159 x^17 - 94 x^18 + 65 x^19 - 29 x^20 + 7 x^21 - x^22)/(1 - 4752830 x^12 + x^24), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 22 2013 *)

Prog

(Magma) I:= 1, 7, 29, 65, 94, 159, 730, 889, 1619, 4127, 18127, 131016, 4734703, 33273937, 137830451, 308934839, 446765290, 755700129, 3469565806, 4225265935, 7694831741, 19614929417, 86154549409, 622696775280]; [n le 24 select I[n] else 4752830*Self(n-12)-Self(n-24): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

Crossrefs

Cf. A041620.

Sequence in context: A080185 A355920 A219835 * A022272 A185438 A265803

Adjacent sequences: A041618 A041619 A041620 * A041622 A041623 A041624

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 22 2013

Status

approved