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A271832
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Period 12 zigzag sequence: repeat [0,1,2,3,4,5,6,5,4,3,2,1].
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10
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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
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OFFSET
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0,3
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COMMENTS
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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
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LINKS
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Table of n, a(n) for n=0..85.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,-1,1).
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FORMULA
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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
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MAPLE
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A271832:=n->[0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1][(n mod 12)+1]: seq(A271832(n), n=0..300);
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MATHEMATICA
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CoefficientList[Series[x*(1 + x + x^2 + x^3 + x^4 + x^5)/(1 - x + x^6 - x^7), {x, 0, 100}], x]
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PROG
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(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
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CROSSREFS
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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.
Sequence in context: A122416 A307784 A134665 * A063260 A271859 A232240
Adjacent sequences: A271829 A271830 A271831 * A271833 A271834 A271835
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KEYWORD
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nonn,easy
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AUTHOR
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Wesley Ivan Hurt, Apr 15 2016
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STATUS
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approved
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