A154811 a(n) = Fibonacci(2*n+1) mod 9.

1, 2, 5, 4, 7, 8, 8, 7, 4, 5, 2, 1, 1, 2, 5, 4, 7, 8, 8, 7, 4, 5, 2, 1, 1, 2, 5, 4, 7, 8, 8, 7, 4, 5, 2, 1, 1, 2, 5, 4, 7, 8, 8, 7, 4, 5, 2, 1, 1, 2, 5, 4, 7, 8, 8, 7, 4, 5, 2, 1, 1, 2, 5, 4, 7, 8, 8, 7, 4, 5, 2, 1

Offset: 0

Author

Paul Curtz, Jan 15 2009

Keywords

• nonn
• easy

Comments

Periodic with period length 12.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,-1,1).

Crossrefs

Cf. A010689, A010875.

Programs

Mathematica

Mod[Fibonacci[Range[1,151,2]],9] (* Harvey P. Dale, Jul 10 2018 *)

PARI

a(n)=fibonacci(n%12*2+1)%9 \\ Charles R Greathouse IV, Dec 21 2011

Formula

a(n) = A001519(n+1) mod 9 = A122367(n) mod 9 = |A099496(n)| mod 9.

From R. J. Mathar, Apr 10 2009: (Start)

a(n) = a(n-1) - a(n-6) + a(n-7).

G.f.: -(1 + x + 3*x^2 - x^3 + 3*x^4 + x^5 + x^6)/((x - 1)*(x^2 + 1)*(x^4 - x^2 + 1)). (End)

Extensions

Edited by R. J. Mathar, Jan 23 2009

Typo in A-number in first formula corrected by R. J. Mathar, Feb 23 2009