A279321 Period 7: repeat [1, 3, 5, 7, 5, 3, 1].

1, 3, 5, 7, 5, 3, 1, 1, 3, 5, 7, 5, 3, 1, 1, 3, 5, 7, 5, 3, 1, 1, 3, 5, 7, 5, 3, 1, 1, 3, 5, 7, 5, 3, 1, 1, 3, 5, 7, 5, 3, 1, 1, 3, 5, 7, 5, 3, 1, 1, 3, 5, 7, 5, 3, 1, 1, 3, 5, 7, 5, 3, 1, 1, 3, 5, 7, 5, 3, 1, 1, 3, 5, 7, 5, 3, 1, 1, 3, 5, 7, 5, 3, 1, 1, 3

Offset: 0

Author

Wesley Ivan Hurt, Dec 09 2016

Keywords

• nonn
• easy

Links

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

Crossrefs

Bisection of A279313.

Programs

Magma

&cat[[1, 3, 5, 7, 5, 3, 1]: n in [0..10]];

Maple

A279321:=n->[1, 3, 5, 7, 5, 3, 1, 1][(n mod 7)+1]: seq(A279321(n), n=0..100); # Wesley Ivan Hurt, Dec 23 2016

Mathematica

PadRight[{}, 120, {1, 3, 5, 7, 5, 3, 1}] (* Vincenzo Librandi, Dec 10 2016 *)
With[{k = 14}, Table[Abs[2 n + 1 - k Round[(2 n + 1)/k]], {n, 0, 120}]] (* Michael De Vlieger, Dec 10 2016 *)

PARI

Vec((1 + 2*x + x^2 + x^3)*(1 + x + 2*x^2 + x^3) / ((1 - x)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)) + O(x^85)) \\ Colin Barker, Mar 21 2019

Formula

a(n) = abs(2n + 1 - 14*round((2n + 1)/14)).

a(n) = (25 + 2*( ((n+1) mod 7) + ((n+2) mod 7) + ((n+3) mod 7) - ((n+4) mod 7) - ((n+5) mod 7) - ((n+6) mod 7) ))/7. - Wesley Ivan Hurt, Dec 23 2016

From Colin Barker, Mar 21 2019: (Start)

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

a(n) = a(n-7) for n>6.

(End)