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A168100
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a(n) = number of natural numbers m such that n - 10 <= m <= n + 10.
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0
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10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21
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OFFSET
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0,1
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COMMENTS
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Generalization: If a(n,k) = number of natural numbers m such that n - k <= m <= n + k (k >= 1) then a(n,k) = a(n-1,k) + 1 = n + k for 0 <= n <= k, a(n,k) = a(n-1,k) = 2k + 1 for n >= k + 1 (see, e.g., A158799). a(n) = 10 + n for 0 <= n <= 10, a(n) = 21 for n >= 11.
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LINKS
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FORMULA
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MATHEMATICA
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CoefficientList[Series[(10 - 9*x - x^12)/(1 - x)^2, {x, 0, 25}], x] (* G. C. Greubel, Jul 12 2016 *)
Table[Count[Range[n-10, n+10], _?Positive], {n, 0, 80}] (* or *) PadRight[ {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}, 120, {21}] (* Harvey P. Dale, Jan 09 2019 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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