A271832 Period 12 zigzag sequence: repeat [0,1,2,3,4,5,6,5,4,3,2,1].

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

Offset: 0

Author

Wesley Ivan Hurt, Apr 15 2016

Keywords

• nonn
• easy

Comments

a(n)/36 is the probability that the sum shown after rolling a pair of standard dice is 1+(n mod 12). - Mathew Englander, Jul 11 2022

Decimal expansion of 37037/3000003. - Elmo R. Oliveira, Mar 03 2024

Links

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

Crossrefs

Period k zigzag sequences: A000035 (k=2), A007877 (k=4), A260686 (k=6), A266313 (k=8), A271751 (k=10), this sequence (k=12), A279313 (k=14), A279319 (k=16), A158289 (k=18).

Cf. A010677, A011655, A110551.

Programs

Magma

&cat[[0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1]: n in [0..10]];

Maple

A271832:=n->[0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1][(n mod 12)+1]: seq(A271832(n), n=0..300);

Mathematica

CoefficientList[Series[x*(1 + x + x^2 + x^3 + x^4 + x^5)/(1 - x + x^6 - x^7), {x, 0, 100}], x]

PARI

lista(nn) = for(n=0, nn, print1(abs(n-12*round(n/12)), ", ")); \\ Altug Alkan, Apr 15 2016

Formula

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

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

a(n) = abs(n - 12*round(n/12)).

a(n) = Sum_{i=1..n} (-1)^floor((i-1)/6).

a(2n) = a(10n) = 2*A260686(n), a(2n+1) = A110551(n).

a(3n) = 3*A007877(n), a(4n) = a(8n) = 4*A011655(n).

a(6n) = A010677(n) = 6*A000035(n).

a(n) = a(n-12) for n >= 12. - Wesley Ivan Hurt, Sep 07 2022