A042140 Numerators of continued fraction convergents to sqrt(595).

24, 49, 73, 122, 561, 683, 3293, 3976, 7269, 18514, 895941, 1810396, 2706337, 4516733, 20773269, 25290002, 121933277, 147223279, 269156556, 685536391, 33174903324, 67035343039, 100210246363

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,37028,0,0,0,0,0,0,0,0,0,-1).

Formula

From Vincenzo Librandi, Nov 18 2013: (Start)

G.f.: (24 +49*x +73*x^2 +122*x^3 +561*x^4 +683*x^5 +3293*x^6 +3976*x^7 +7269*x^8 +18514*x^9 +7269*x^10 -3976*x^11 +3293*x^12 -683*x^13 +561*x^14 -122*x^15 +73*x^16 -49*x^17 +24*x^18 -x^19)/(1 -37028*x^10 +x^20).

a(n) = 37028*a(n-10) - a(n-20). (End)

Mathematica

Numerator[Convergents[Sqrt[595], 30]] (* or *) CoefficientList[Series[(24 + 49 x + 73 x^2 + 122 x^3 + 561 x^4 + 683 x^5 + 3293 x^6 + 3976 x^7 + 7269 x^8 + 18514 x^9 + 7269 x^10 - 3976 x^11 + 3293 x^12 - 683 x^13 + 561 x^14 - 122 x^15 + 73 x^16 - 49 x^17 + 24 x^18 - x^19)/(1 - 37028 x^10 + x^20), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 18 2013 *)

Prog

(Magma) I:=[24, 49, 73, 122, 561, 683, 3293, 3976, 7269, 18514, 895941, 1810396, 2706337, 4516733, 20773269, 25290002, 121933277, 147223279, 269156556, 685536391]; [n le 20 select I[n] else 37028*Self(n-10)-Self(n-20): n in [1..30]]; // Vincenzo Librandi, Nov 18 2013

Crossrefs

Cf. A042141.

Sequence in context: A352699 A105844 A129837 * A042138 A042136 A043366

Adjacent sequences: A042137 A042138 A042139 * A042141 A042142 A042143

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved