A041202 - OEIS

%I #16 Jun 13 2015 00:49:22

%S 10,11,21,53,74,127,2614,2741,5355,13451,18806,32257,663946,696203,

%T 1360149,3416501,4776650,8193151,168639670,176832821,345472491,

%U 867777803,1213250294,2081028097,42833812234

%N Numerators of continued fraction convergents to sqrt(112).

%H Vincenzo Librandi, <a href="/A041202/b041202.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,254,0,0,0,0,0,-1).

%F 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]

%t Numerator[Convergents[Sqrt[112], 30]] (* _Vincenzo Librandi_, Oct 26 2013 *)

%o (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

%Y Cf. A041203.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.