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A173151
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a(n) = a(n-1) - [a(n-1)/2] + a(n-2) - [a(n-5)/2] where [k] = floor(k).
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6
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1, 1, 2, 2, 3, 4, 5, 6, 7, 9, 10, 12, 13, 16, 17, 20, 21, 25, 26, 30, 31, 36, 37, 42, 43, 49, 50, 56, 57, 64, 65, 72, 73, 81, 82, 90, 91, 100, 101, 110, 111, 121, 122, 132, 133, 144, 145, 156, 157, 169, 170
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = a(n-1)-floor[a(n-1)/2]+a(n-2)-floor[a(n-5)/2].
a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-4) - a(n-5) - a(n-6) + a(n-7) for n > 6.
G.f.: (-x^5 + x^4 - 1)/((x - 1)^3*(x + 1)^2*(x^2 + 1)). (End)
a(n) = ((-1)^n*(11 - 2*n) + 2*n*(n + 5) + 4*sin(Pi*n/2) - 4*cos(Pi*n/2) + 25)/32. - Ilya Gutkovskiy, Jun 03 2016
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MATHEMATICA
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f[-3] = 0; f[-2] = 0; f[-1] = 0; f[0] = 1; f[1] = 1;
f[n_] := f[n] = f[n - 1] + f[n - 2] - Floor[f[n - 1]/2] - Floor[f[n - 5]/2]
Table[f[n], {n, 0, 50}]
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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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