A279316 Period 7: repeat [0, 1, 2, 3, 3, 2, 1].

0, 1, 2, 3, 3, 2, 1, 0, 1, 2, 3, 3, 2, 1, 0, 1, 2, 3, 3, 2, 1, 0, 1, 2, 3, 3, 2, 1, 0, 1, 2, 3, 3, 2, 1, 0, 1, 2, 3, 3, 2, 1, 0, 1, 2, 3, 3, 2, 1, 0, 1, 2, 3, 3, 2, 1, 0, 1, 2, 3, 3, 2, 1, 0, 1, 2, 3, 3, 2, 1, 0, 1, 2, 3, 3, 2, 1, 0, 1, 2, 3, 3, 2, 1, 0, 1

Offset: 0

Author

Wesley Ivan Hurt, Dec 09 2016

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A279313.

Cf. A010876.

Programs

Magma

&cat[[0, 1, 2, 3, 3, 2, 1]: n in [0..10]];

Maple

a:=n->[0, 1, 2, 3, 3, 2, 1][(n mod 7)+1]: seq(a(n), n=0..300);

Mathematica

CoefficientList[Series[x*(1 + 2*x + 3*x^2 + 3*x^3 + 2*x^4 + x^5)/(1 - x^7), {x, 0, 100}], x]
PadRight[{}, 120, {0, 1, 2, 3, 3, 2, 1}] (* Vincenzo Librandi, Dec 10 2016 *)

Formula

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

a(n) = (1/2) * Sum_{i=1..2n} (-1)^floor((i-1)/7).

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

a(n) = A279313(2n)/2.

a(n) = -m*(m^5 - 21*m^4 + 160*m^3 - 525*m^2 + 739*m - 714)/360 where m = n mod 7. - Luce ETIENNE, Nov 18 2018