A154629 Period 9: repeat [9, 3, 1, 3, 3, 1, 3, 9, 1].

9, 3, 1, 3, 3, 1, 3, 9, 1, 9, 3, 1, 3, 3, 1, 3, 9, 1, 9, 3, 1, 3, 3, 1, 3, 9, 1, 9, 3, 1, 3, 3, 1, 3, 9, 1, 9, 3, 1, 3, 3, 1, 3, 9, 1, 9, 3, 1, 3, 3, 1, 3, 9, 1, 9, 3, 1, 3, 3, 1, 3, 9, 1, 9, 3, 1, 3, 3, 1, 3, 9, 1, 9, 3, 1, 3, 3, 1, 3, 9, 1, 9, 3, 1, 3, 3

Offset: 0

Author

Paul Curtz, Jan 13 2009

Keywords

• nonn
• easy

Comments

Greatest common divisor of (n+1)^2-1 and (n+1)^2+8. - Bruno Berselli, Mar 08 2017

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1).

Crossrefs

Cf. A005563, A144454, A147674.

Programs

Mathematica

With[{n=5}, PadLeft[{}, 9n, {9,3,1,3,3,1,3,9,1}]] (* Harvey P. Dale, Oct 22 2011 *)

PARI

Vec((9 + 3*x + x^2 + 3*x^3 + 3*x^4 + x^5 + 3*x^6 + 9*x^7 + x^8) / ((1 - x)*(1 + x + x^2)*(1 + x^3 + x^6)) + O(x^100)) \\ Colin Barker, Dec 21 2017

Formula

a(n) = A147674(n)/9.

a(n) = A005563(n) / A144454(n+1) for n>0.

From Colin Barker, Dec 21 2017: (Start)

G.f.: (9 + 3*x + x^2 + 3*x^3 + 3*x^4 + x^5 + 3*x^6 + 9*x^7 + x^8) / ((1 - x)*(1 + x + x^2)*(1 + x^3 + x^6)).

a(n) = a(n-9) for n>8.

(End)