A167398 a(n) = Fibonacci(11*n).

0, 89, 17711, 3524578, 701408733, 139583862445, 27777890035288, 5527939700884757, 1100087778366101931, 218922995834555169026, 43566776258854844738105, 8670007398507948658051921, 1725375039079340637797070384, 343358302784187294870275058337, 68330027629092351019822533679447

Offset

0,2

Links

Table of n, a(n) for n=0..14.

Index entries for linear recurrences with constant coefficients, signature (199,1).

Formula

a(n) = 199*a(n-1) + a(n-2) for n > 1; a(0)=0, a(1)=89.

From Elmo R. Oliveira, Mar 29 2026: (Start)

G.f.: 89*x/(1 - 199*x - x^2).

a(n) = 89*A305413(n) = A000045(A008593(n)). (End)

Sum_{n>=1} (-1)^(n+1)/(a(n)*a(n+1)) = (89*sqrt(5)-199)/15842. - Amiram Eldar, Apr 06 2026

Mathematica

Table[Fibonacci[11k], {k, 0, 20}]
(* Alternative: *)
{a, b}={0, 89}; Do[Print[c={a, b}.{1, 199}]; a=b; b=c, {20}]

Prog

(Magma) [Fibonacci(11*n): n in [0..100]]; // Vincenzo Librandi, Apr 17 2011

Crossrefs

Cf. A000045, A008593, A134498 (Fibonacci(7*n)), A305413.

Sequence in context: A056568 A174758 A181681 * A023330 A059766 A033513

Adjacent sequences: A167395 A167396 A167397 * A167399 A167400 A167401

Keyword

nonn,easy

Author

Zak Seidov, Nov 02 2009

Status

approved