A041126 - OEIS

%I #28 Jul 14 2015 16:53:14

%S 8,17,280,577,9512,19601,323128,665857,10976840,22619537,372889432,

%T 768398401,12667263848,26102926097,430314081400,886731088897,

%U 14618011503752,30122754096401,496582077046168,1023286908188737,16869172608065960,34761632124320657

%N Numerators of continued fraction convergents to sqrt(72).

%H Vincenzo Librandi, <a href="/A041126/b041126.txt">Table of n, a(n) for n = 0..100</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,34,0,-1).

%F G.f.: -(x+1)*(x^2-9*x-8) / ((x^2-6*x+1)*(x^2+6*x+1)). - _Colin Barker_, Nov 05 2013

%F From _Gerry Martens_, Jul 11 2015: (Start)

%F Interspersion of 2 sequences [a1(n),a0(n)] for n>0:

%F a0(n) = (-4+3*sqrt(2))*(17+12*sqrt(2))^n-((4+3*sqrt(2))/(17+12*sqrt(2))^n).

%F a1(n) = (1/(17+12*sqrt(2))^n+(17+12*sqrt(2))^n)/2. (End)

%t Numerator[Convergents[Sqrt[72], 30]] (* _Vincenzo Librandi_, Oct 29 2013 *)

%t a0[n_] := (-4+3*Sqrt[2])*(17+12*Sqrt[2])^n-((4+3*Sqrt[2])/(17+12*Sqrt[2])^n) // Simplify

%t a1[n_] := (1/(17+12*Sqrt[2])^n+(17+12*Sqrt[2])^n)/2 // FullSimplify

%t Flatten[MapIndexed[{a0[#], a1[#]} &, Range[20]]] (* _Gerry Martens_, Jul 11 2015 *)

%Y Cf. A010524, A041127.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_

%E More terms from _Colin Barker_, Nov 05 2013