%I #35 Sep 26 2016 08:55:32

%S 1,161,34561,8346401,2150012161,576914365601,44861726436508961,

%T 12840299190293644801,3721082815965949056161,

%U 321507757074243457409731361,28572486227889263832443550935201,8586901708088882505643582648796161

%N Numbers of the form Fibonacci(12n)/(144n).

%C The last two digits end either in 01 or 61. Digital root alternates 1 and 8.

%C Consecutive terms have ratios that approximate the product of Golden Ratio powers of multiples of 12 and consecutive integers fractions: E.g., the 4th term divided by the 3rd term approximates Golden Ratio^12 * 3/4; the 10th term divided by the 9th term approximates Golden Ratio^24 * 5/6; and the 16th term divided by the 15 term is a close approximation of Golden Ratio^48 * 5/6, etc.

%F a(n) = Integer Values of Fib(12n)/(144n)

%e a(3) = Fib(12*3)/(144*3) = Fib36 / 432 = 34561; therefore, the third term is integer 34561.

%t Select[Table[Fibonacci[12n]/(144n),{n,20}],IntegerQ] (* _Harvey P. Dale_, Sep 26 2016 *)

%o (PARI) for(n=1,100, t=fibonacci(12*n)/144/n; if(denominator(t)==1, print1(t", "))) \\ _Charles R Greathouse IV_, Apr 30 2016

%Y Cf. A072378.

%K nonn,easy

%O 1,2

%A _Peter M. Chema_, Apr 29 2016