A041675 Denominators of continued fraction convergents to sqrt(356).

1, 1, 7, 8, 15, 38, 53, 462, 515, 1492, 2007, 3499, 23001, 26500, 977001, 1003501, 6998007, 8001508, 14999515, 38000538, 53000053, 462000962, 515001015, 1492002992, 2007004007, 3499006999, 23001046001, 26500053000, 977002954001, 1003503007001

Offset

0,3

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, 0, 0, 1000002, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^26 -x^25 +7*x^24 -8*x^23 +15*x^22 -38*x^21 +53*x^20 -462*x^19 +515*x^18 -1492*x^17 +2007*x^16 -3499*x^15 +23001*x^14 -26500*x^13 -23001*x^12 -3499*x^11 -2007*x^10 -1492*x^9 -515*x^8 -462*x^7 -53*x^6 -38*x^5 -15*x^4 -8*x^3 -7*x^2 -x -1)/(x^28 -1000002*x^14 +1). - Vincenzo Librandi, Dec 22 2013

a(n) = 1000002*a(n-14) - a(n-28) for n>27. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[356], 30]] (* or *) CoefficientList[Series[-(x^26 - x^25 + 7 x^24 - 8 x^23 + 15 x^22 - 38 x^21 + 53 x^20 - 462 x^19 + 515 x^18 - 1492 x^17 + 2007 x^16 - 3499 x^15 + 23001 x^14 - 26500 x^13 - 23001 x^12 - 3499 x^11 - 2007 x^10 - 1492 x^9 - 515 x^8 - 462 x^7 - 53 x^6 - 38 x^5 - 15 x^4 - 8 x^3 - 7 x^2 - x - 1)/(x^28 - 1000002 x^14 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 22 2013 *)

Crossrefs

Cf. A041674.

Sequence in context: A191413 A066971 A084377 * A041098 A041427 A042755

Adjacent sequences: A041672 A041673 A041674 * A041676 A041677 A041678

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 22 2013

Status

approved