A111952 a(n) = 3*n mod 7.

0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1

Offset: 0

Author

Paul Barry, Aug 22 2005

Keywords

• easy
• nonn

Comments

Period 7: repeat [0, 3, 6, 2, 5, 1, 4].

Draw a regular heptagon with vertices labeled 0..6 going clockwise. Choose any seven consecutive values of a(n) and connect the corresponding vertices in that order with straight lines. This results in a clockwise-inscribed seven-pointed star that remains unbroken during construction. - Wesley Ivan Hurt, Apr 10 2015

Links

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

Crossrefs

Cf. A022264.

Programs

Magma

[3*n mod 7 : n in [0..100]]; // Wesley Ivan Hurt, Apr 10 2015

Maple

A111952:=n->3*n mod 7: seq(A111952(n), n=0..100); # Wesley Ivan Hurt, Apr 10 2015

Mathematica

Mod[3 Range[0, 100], 7] (* Wesley Ivan Hurt, Apr 10 2015 *)

PARI

a(n)=3*n%7 \\ Charles R Greathouse IV, Jul 23 2011

Formula

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

a(n) = mod(n*(7*n-1)/2, 7) = mod(A022264(n), 7).

Recurrence: a(n) = a(n-7) for n > 6. - Wesley Ivan Hurt, Apr 10 2015

a(n) = (21 + 4*(n mod 7) - 3*((n+1) mod 7) + 4*((n+2) mod 7) - 3*((n+3) mod 7) + 4*((n+4) mod 7) - 3*((n+5) mod 7) - 3*((n+6) mod 7))/7. - Wesley Ivan Hurt, Dec 23 2016

a(n) = A010876(3*n). - R. J. Mathar, Jan 15 2021