A157696 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).

31, 2521, 97921, 4974481, 226965751, 10783342081, 504420084871, 23735900452321, 1114384154071681, 52364857850613001, 2459808940392975631, 115562692701892638721, 5428914300540041959471, 255044709450472227347881

Offset: 1

Author

Carmine Suriano, Mar 04 2009

Keywords

• nonn

Comments

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

Crossrefs

A000204, A110391, A000045

Programs

Maple

Contribution from R. J. Mathar, Oct 18 2010: (Start)
A005248 := proc(n) combinat[fibonacci](2*n-1)+combinat[fibonacci](2*n+1) ; end proc:
A110391 := proc(n) A005248(n)-(-1)^n ; end proc:
A157696 := proc(n) A110391(5*n)/A110391(n) ; end proc: seq(A157696(n),n=1..25) ; (End)

Formula

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]

Extensions

a(1) replaced by 31 - R. J. Mathar, Oct 18 2010