OFFSET
0,2
COMMENTS
Decimal expansion of 111111112/900000009.
For n which lies in the interval [16*(k-1), 8*(2*k-1)], where k>0 -> pattern {1, 2, 3, 4, 5, 6, 7, 8, 9}; for n which lies in the interval [16*k - 7, 16*k - 1], where k>0 -> pattern {8, 7, 6, 5, 4, 3, 2}.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,-1,1).
FORMULA
-1 + a(16*(k - 1)) = -2 + a(8*k + 3*(-1)^k - 4) = -3 + a(2*(4*k + (-1)^k - 2)) = -4 + a(8*k + (-1)^k - 4) = -5 + a(4*(2*k - 1)) = -6 + a(8*k - (-1)^k - 4) = -7 + a(-2*(-4*k + (-1)^k + 2)) = -8 + a(8*k - 3*(-1)^k - 4) = -9 + a(8*(2*k - 11)) = 0, for k>0.
a(0) = 1, a(n) = a(n+1) - 1, for 16*(k - 1) <= n < 8*(2*k - 1), and a(n) = a(n + 1) + 1, for (8*(2*k - 1) <= n < 16*(k-1), where k>0.
From Colin Barker, Sep 29 2015: (Start)
a(n) = a(n-1) - a(n-8) + a(n-9) for n>8.
G.f.: -(2*x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1) / ((x-1)*(x^8+1)).
(End)
MATHEMATICA
LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, -1 , 1}, {1, 2, 3, 4, 5, 6, 7, 8, 9}, 120] (* Vincenzo Librandi, Sep 29 2015 *)
PROG
(PARI) Vec(-(2*x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1)/((x-1)*(x^8+1)) + O(x^100)) \\ Colin Barker, Sep 29 2015
(Magma) &cat[[1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2]: n in [0..10]]; // Vincenzo Librandi, Sep 29 2015
(PARI) 111111112/900000009. \\ Altug Alkan, Sep 29 2015
(PARI) vector(200, n, default(realprecision, n+2); floor(111111112/900000009*10^n)%10) \\ Altug Alkan, Nov 12 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Sep 29 2015
STATUS
approved