A042668 Numerators of continued fraction convergents to sqrt(864).

29, 59, 88, 147, 823, 970, 13433, 14403, 85448, 99851, 185299, 470449, 27471341, 55413131, 82884472, 138297603, 774372487, 912670090, 12639083657, 13551753747, 80397852392, 93949606139, 174347458531, 442644523201, 25847729804189, 52138104131579

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,940898,0,0,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^23 -29*x^22 +59*x^21 -88*x^20 +147*x^19 -823*x^18 +970*x^17 -13433*x^16 +14403*x^15 -85448*x^14 +99851*x^13 -185299*x^12 -470449*x^11 -185299*x^10 -99851*x^9 -85448*x^8 -14403*x^7 -13433*x^6 -970*x^5 -823*x^4 -147*x^3 -88*x^2 -59*x -29) / ((x^4 -6*x^3 +13*x^2 -6*x +1)*(x^4 -10*x^2 +1)*(x^4 +10*x^2 +1)*(x^4 +6*x^3 +13*x^2 +6*x +1)*(x^8 +10*x^6 +99*x^4 +10*x^2 +1)). - Colin Barker, Dec 20 2013

a(n) = 940898*a(n-12)-a(n-24). - Wesley Ivan Hurt, Apr 26 2021

Mathematica

Numerator[Convergents[Sqrt[864], 30]] (* Vincenzo Librandi, Nov 30 2013 *)

Crossrefs

Cf. A042669, A040834.

Sequence in context: A055784 A083821 A042666 * A042664 A042662 A128469

Adjacent sequences: A042665 A042666 A042667 * A042669 A042670 A042671

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 20 2013

Status

approved