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0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10, 10, 11, 11, 12, 12, 12, 13, 13, 14, 14, 14, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 22, 22, 22, 23, 23, 24, 24, 24, 25, 25, 26, 26, 26, 27, 27, 28, 28, 28, 29, 29, 30, 30
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OFFSET
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0,6
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COMMENTS
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The cyclic pattern (and numerator of the gf) is computed using Euclid's algorithm for GCD.
The sequence a(n) can be used in determining confidence intervals for the median of a population. Let Y(i) denote the i-th smallest datum in a random sample of size n from any population of values. When estimating the population median with a symmetric interval [Y(r), Y(n-r+1)], the exact confidence coefficient c for the interval is given by c=sum(C(n, k)(1/2)^n,k=r..n-r). If r = a(n-4), then the confidence coefficient will be (i) at least 0.90 for all n>=7, (ii) at least 0.95 for all n>=35, and (iii) at least 0.99 for all n>=115. To use the sequence, for example, decide on the minimum level of confidence desired, say 95%. Hence use a sample size of 35 or greater, say n=40. We then find a(n-4)=a(36)=14, and thus the 14th smallest and 14th largest values in the sample will form the bounds for the confidence interval. If the exact confidence coefficient c is needed, calculate c=sum(C(40,k)(1/2)^40, k=14..26), which is 0.9615226917. [From Dennis P. Walsh, Nov 28 2011]
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REFERENCES
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N. Dershowitz and E. M. Reingold, Calendrical Calculations, Cambridge University Press, 1997.
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, NY, 1994.
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LINKS
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Table of n, a(n) for n=0..76.
N. Dershowitz and E. M. Reingold, Calendrical Calculations Web Site
Dennis Walsh, Median estimation with the point-four-n-minus-two rule
Index to sequences with linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).
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FORMULA
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G.f.: x^3*(1+x^2) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - Numerator corrected by R. J. Mathar, Feb 20 2011
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PROG
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(PARI) a(n)=2*n\5 \\ Charles R Greathouse IV, Nov 28 2011
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CROSSREFS
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Floors of other ratios: A004526, A002264, A002265, A004523, A057353, A057354, A057355, A057356, A057357, A057358, A057359, A057360, A057361, A057362, A057363, A057364, A057365, A057366, A057367.
Sequence in context: A061375 A029920 A100719 * A172476 A172267 A097508
Adjacent sequences: A057351 A057352 A057353 * A057355 A057356 A057357
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KEYWORD
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nonn,easy,changed
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AUTHOR
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Mitch Harris
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STATUS
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approved
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