A157696 - OEIS

%I #4 Mar 30 2012 17:39:54

%S 31,2521,97921,4974481,226965751,10783342081,504420084871,

%T 23735900452321,1114384154071681,52364857850613001,

%U 2459808940392975631,115562692701892638721,5428914300540041959471,255044709450472227347881

%N Define k(n) to be the sequence of integers such that k(n)F(n)=F(2n)(Fibonacci sequence) (A000204); in turn define g(n) to be the sequence of integers such that g(n)k(n)=k(3n)(A110391); finally a(n) is the sequence of integers such that a(n)g(n)=g(5n).

%C Indices 2 of F(i), 3 of k(i) and 5 of g(i) are the minimum integers that provide sequences of integers.

%F a(n) = A110391(5*n)/A110391(n) = 27*a(n-1) +904*a(n-2) +1660*a(n-3) -1660*a(n-4) -904*a(n-5) -27*a(n-6) +a(n-7). [From _R. J. Mathar_, Oct 18 2010]

%p Contribution from _R. J. Mathar_, Oct 18 2010: (Start)

%p A005248 := proc(n) combinat[fibonacci](2*n-1)+combinat[fibonacci](2*n+1) ; end proc:

%p A110391 := proc(n) A005248(n)-(-1)^n ; end proc:

%p A157696 := proc(n) A110391(5*n)/A110391(n) ; end proc: seq(A157696(n),n=1..25) ; (End)

%Y A000204, A110391, A000045

%K nonn

%O 1,1

%A _Carmine Suriano_, Mar 04 2009

%E a(1) replaced by 31 - _R. J. Mathar_, Oct 18 2010