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A173329
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a(n) = a(n-2) + a(n-3) - floor(a(n-3)/2) - floor(a(n-6)/2).
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1
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1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 8, 8, 10, 10, 11, 12, 12, 14, 13, 15, 15, 16, 17, 17, 19, 19, 21, 21, 23, 24, 25, 27, 27, 30, 30, 32, 33, 34, 36, 36, 38, 38, 40, 40, 41, 42, 42, 44, 43, 45, 45, 46, 47, 47, 49, 49, 51, 51, 53, 54, 55, 57, 57, 60, 60, 62, 63
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OFFSET
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0,4
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COMMENTS
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This sequence is interesting because in the graph of a(n+1)/a(n) there are four modes all approaching one at different rates.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,1,-1).
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FORMULA
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a(n+30) = a(n)+30 for n>=12.
a(n) = a(n-1) + a(n-2) - a(n-4) - a(n-6) + a(n-8) + a(n-9) - a(n-10) for n > 21.
G.f.: (x^21 - x^20 + x^18 - x^16 + x^14 - x^13 + x^11 - x^9 + x^7 - x^2 + 1)/(x^10 - x^9 - x^8 + x^6 + x^4 - x^2 - x + 1). (End)
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MATHEMATICA
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f[-4] = 0; f[-3] = 0; f[-2] = 0; f[-1] = 0; f[0] = 1; f[1] = 1;
f[n_] := f[n] = f[n - 2] + f[n - 3] - Floor[f[n - 3]/2] - Floor[f[n - 6]/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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EXTENSIONS
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STATUS
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approved
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