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A021893
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Decimal expansion of 1/889.
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0
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0, 0, 1, 1, 2, 4, 8, 5, 9, 3, 9, 2, 5, 7, 5, 9, 2, 8, 0, 0, 8, 9, 9, 8, 8, 7, 5, 1, 4, 0, 6, 0, 7, 4, 2, 4, 0, 7, 1, 9, 9, 1, 0, 0, 1, 1, 2, 4, 8, 5, 9, 3, 9, 2, 5, 7, 5, 9, 2, 8, 0, 0, 8, 9, 9, 8, 8, 7, 5, 1, 4, 0, 6, 0, 7, 4, 2, 4, 0, 7, 1, 9, 9, 1, 0, 0, 1, 1, 2, 4, 8, 5, 9, 3, 9, 2, 5, 7, 5
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OFFSET
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0,5
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COMMENTS
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Sum_{i=0}^{infty} [tribonacci(i) / 10^(i+1)].
Generalization: [since tribonacci(i+3) =
tribonacci(i+2) + tribonacci(i+1) + tribonacci(i)]
1/889 = Sum_{i=0}^{infty} [tribonacci(i) / 10^(i+1)], (this sequence)
1/989899 = Sum_{i=0}^{infty} [tribonacci(i) / 100^(i+1)],
1/998998999 = Sum_{i=0}^{infty} [tribonacci(i) / 1000^(i+1)],
1/999899989999 = Sum_{i=0}^{infty} [tribonacci(i) / 10000^(i+1)],
...
1 / [(10^k)^3 - (10^k)^2 - (10^k)^1 - (10^k)^0] = 1 / [10^(3k) - 10^(2k) - 10^k - 1] = Sum_{i=0}^{infty} [tribonacci(i) / (10^k)^{i+1}], k >= 1. - Daniel Forgues, May 04 2013
Sum_{i=0}^{infty} [111^i / 1000^(i+1)].
Generalization: [since 111^(i+1) = 111 * 111^(i)]
1/889 = Sum_{i=0}^{infty} [111^i / 1000^(i+1)], (this sequence)
1/9889 = Sum_{i=0}^{infty} [111^i / 10000^(i+1)],
1/99889 = Sum_{i=0}^{infty} [111^i / 100000^(i+1)],
1/999889 = Sum_{i=0}^{infty} [111^i / 1000000^(i+1)],
...
1 / [(10^k)^1 - 111 (10^k)^0] = 1 / [10^k - 111] =
Sum_{i=0}^{infty} [111^i / (10^k)^(i+1)], k >= 3.
- Daniel Forgues, May 04 2013
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LINKS
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Table of n, a(n) for n=0..98.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1).
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FORMULA
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From Chai Wah Wu, Feb 03 2021: (Start)
a(n) = a(n-1) - a(n-21) + a(n-22) for n > 21.
G.f.: (-x^21 - 8*x^20 + 8*x^18 - 6*x^17 + 7*x^16 - 4*x^15 + 2*x^14 - 2*x^13 - 3*x^12 + 7*x^11 - 6*x^10 + 6*x^9 - 4*x^8 + 3*x^7 - 4*x^6 - 2*x^5 - x^4 - x^2)/(x^22 - x^21 + x - 1). (End)
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MATHEMATICA
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Join[{0, 0}, RealDigits[1/889, 10, 120][[1]]] (* or *) PadRight[{}, 120, {0, 0, 1, 1, 2, 4, 8, 5, 9, 3, 9, 2, 5, 7, 5, 9, 2, 8, 0, 0, 8, 9, 9, 8, 8, 7, 5, 1, 4, 0, 6, 0, 7, 4, 2, 4, 0, 7, 1, 9, 9, 1}] (* Harvey P. Dale, Dec 02 2018 *)
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CROSSREFS
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Cf. A000073.
Sequence in context: A165669 A227818 A300890 * A036117 A307357 A116624
Adjacent sequences: A021890 A021891 A021892 * A021894 A021895 A021896
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KEYWORD
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nonn,cons
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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