OFFSET
0,3
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).
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(n) = a(n-12) for n >= 12. - Wesley Ivan Hurt, Sep 07 2022
MATHEMATICA
CoefficientList[Series[x*(1 + x + x^2 + x^3 + x^4 + x^5)/(1 - x + x^6 - x^7), {x, 0, 100}], x]
PROG
(Magma) &cat[[0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1]: n in [0..10]];
(PARI) lista(nn) = for(n=0, nn, print1(abs(n-12*round(n/12)), ", ")); \\ Altug Alkan, Apr 15 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Apr 15 2016
STATUS
approved