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A042024 Numerators of continued fraction convergents to sqrt(536). 2
23, 139, 162, 301, 764, 4121, 9006, 13127, 22133, 145925, 6734683, 40554023, 47288706, 87842729, 222974164, 1202713549, 2628401262, 3831114811, 6459516073, 42588211249, 1965517233527, 11835691612411 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,291850,0,0,0,0,0,0,0,0,0,-1).

FORMULA

G.f.: (23 +139*x +162*x^2 +301*x^3 +764*x^4 +4121*x^5 +9006*x^6 +13127*x^7 +22133*x^8 +145925*x^9 +22133*x^10 -13127*x^11 +9006*x^12 -4121*x^13 +764*x^14 -301*x^15 +162*x^16 -139*x^17 +23*x^18 -x^19) / (1 -291850*x^10 +x^20). - Vincenzo Librandi, Nov 13 2013

a(n) = 291850*a(n-10)-a(n-20): n in [1..30]]; // Vincenzo Librandi, Nov 14 2013

MATHEMATICA

Numerator[Convergents[Sqrt[536], 30]] (* or *) CoefficientList[Series[(23 + 139 x + 162 x^2 + 301 x^3 + 764 x^4 + 4121 x^5 + 9006 x^6 + 13127 x^7 + 22133 x^8 + 145925 x^9 + 22133 x^10 - 13127 x^11 + 9006 x^12 - 4121 x^13 + 764 x^14 - 301 x^15 + 162 x^16 - 139 x^17 + 23 x^18 - x^19)/(1 - 291850 x^10 + x^20), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 14 2013 *)

PROG

(MAGMA) I:=[23, 139, 162, 301, 764, 4121, 9006, 13127, 22133, 145925, 6734683, 40554023, 47288706, 87842729, 222974164, 1202713549, 2628401262, 3831114811, 6459516073, 42588211249]; [n le 20 select I[n] else 291850*Self(n-10)-Self(n-20): n in [1..30]]; // Vincenzo Librandi, Nov 14 2013

CROSSREFS

Cf. A042025.

Sequence in context: A254758 A057883 A160221 * A141999 A059915 A059701

Adjacent sequences:  A042021 A042022 A042023 * A042025 A042026 A042027

KEYWORD

nonn,cofr,frac,easy,less

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 15 22:28 EST 2019. Contains 320138 sequences. (Running on oeis4.)