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A174738
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Partial sums of floor(n/7).
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17
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0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 15, 17, 19, 21, 24, 27, 30, 33, 36, 39, 42, 46, 50, 54, 58, 62, 66, 70, 75, 80, 85, 90, 95, 100, 105, 111, 117, 123, 129, 135, 141, 147, 154, 161, 168, 175, 182, 189, 196, 204, 212, 220, 228, 236
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OFFSET
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0,9
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COMMENTS
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Apart from the initial zeros, the same as A011867.
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LINKS
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FORMULA
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a(n) = round(n*(n-5)/14).
a(n) = floor((n-2)*(n-3)/14).
a(n) = ceiling((n+1)*(n-6)/14).
a(n) = a(n-7) + n - 6, n > 6.
a(n) = +2*a(n-1) - a(n-2) + a(n-7) - 2*a(n-8) + a(n-9). - R. J. Mathar, Nov 30 2010
G.f.: x^7/( (1 + x + x^2 + x^3 + x^4 + x^5 + x^6)*(1-x)^3 ). - R. J. Mathar, Nov 30 2010
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EXAMPLE
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a(9) = floor(0/7) + floor(1/7) + floor(2/7) + floor(3/7) + floor(4/7) + floor(5/7) + floor(6/7) + floor(7/7) + floor(8/7) + floor(9/7) = 3.
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MAPLE
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A174738 := proc(n) round(n*(n-5)/14) ; end proc:
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MATHEMATICA
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Table[Floor[(n - 2)*(n - 3)/14], {n, 0, 60}] (* G. C. Greubel, Dec 13 2016 *)
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PROG
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(Sage) [floor((n-2)*(n-3)/14) for n in (0..60)] # G. C. Greubel, Aug 31 2019
(GAP) List([0..60], n-> Int((n-2)*(n-3)/14)); # G. C. Greubel, Aug 31 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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