A041202 Numerators of continued fraction convergents to sqrt(112).

10, 11, 21, 53, 74, 127, 2614, 2741, 5355, 13451, 18806, 32257, 663946, 696203, 1360149, 3416501, 4776650, 8193151, 168639670, 176832821, 345472491, 867777803, 1213250294, 2081028097, 42833812234

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,254,0,0,0,0,0,-1).

Formula

a(n) = 254*a(n-6)-a(n-12). G.f.: -(x^11-10*x^10+11*x^9-21*x^8+53*x^7-74*x^6-127*x^5-74*x^4-53*x^3-21*x^2-11*x-10)/((x^6-16*x^3+1)*(x^6+16*x^3+1)). [Colin Barker, Jul 19 2012]

Mathematica

Numerator[Convergents[Sqrt[112], 30]] (* Vincenzo Librandi, Oct 26 2013 *)

Prog

(PARI) A041202(Nmax=99)=Vec(O(x^Nmax)+(10+11*x+21*x^2+53*x^3+74*x^4+127*x^5+74*x^6-53*x^7+21*x^8-11*x^9+10*x^10-x^11)/(1-254*x^6+x^12)) \\ - M. F. Hasler, Oct 26 2013

Crossrefs

Cf. A041203.

Sequence in context: A022100 A041475 A041204 * A324550 A214617 A041200

Adjacent sequences: A041199 A041200 A041201 * A041203 A041204 A041205

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved