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
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).
Programs
-
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 *)
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]
Extensions
Formula corrected by Colin Barker, Jul 24 2012