A041134 Numerators of continued fraction convergents to sqrt(76).

8, 9, 26, 35, 61, 340, 1421, 7445, 8866, 16311, 41488, 57799, 966272, 1024071, 3014414, 4038485, 7052899, 39302980, 164264819, 860627075, 1024891894, 1885518969, 4795929832, 6681448801, 111699110648

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,115598,0,0,0,0,0,0,0,0,0,0,0,-1).

Formula

a(n) = 115598*a(n-12)-a(n-24). G.f.: -(x^23 -8*x^22 +9*x^21 -26*x^20 +35*x^19 -61*x^18 +340*x^17 -1421*x^16 +7445*x^15 -8866*x^14 +16311*x^13 -41488*x^12 -57799*x^11 -41488*x^10 -16311*x^9 -8866*x^8 -7445*x^7 -1421*x^6 -340*x^5 -61*x^4 -35*x^3 -26*x^2 -9*x-8) /( (x^12-340*x^6+1)*(x^12+340*x^6+1) ). [Colin Barker, Jul 19 2012]

Mathematica

Numerator[Convergents[Sqrt[76], 30]] (* Harvey P. Dale, Aug 24 2011 *)
CoefficientList[Series[- (x^23 - 8 x^22 + 9 x^21 - 26 x^20 + 35 x^19 - 61 x^18 + 340 x^17 - 1421 x^16 + 7445 x^15 - 8866 x^14 + 16311 x^13 - 41488 x^12 - 57799 x^11 - 41488 x^10 - 16311 x^9 - 8866 x^8 - 7445 x^7 - 1421 x^6 - 340 x^5 - 61 x^4 - 35 x^3 - 26 x^2 - 9 x - 8)/((x^12 - 340 x^6 + 1) (x^12 + 340 x^6 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 26 2013 *)

Crossrefs

Cf. A010528, A041135.

Sequence in context: A173745 A305828 A322652 * A108219 A041317 A305336

Adjacent sequences: A041131 A041132 A041133 * A041135 A041136 A041137

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

Formula corrected by Colin Barker, Jul 24 2012

Status

approved