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A283904
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Relative of Hofstadter Q-sequence: a(1) = 1, a(2) = 1; thereafter a(n) = a(n-2a(n-1)) + a(n-3a(n-2)).
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1
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1, 1, 1, 2, 2, 1, 3, 3, 1, 4, 4, 2, 2, 7, 2, 2, 6, 3, 3, 11, 2, 3, 12, 2, 2, 14, 2, 2, 14, 3, 2, 14, 4, 14, 15, 1, 15, 18, 1, 18, 20, 1, 20, 22, 1, 22, 23, 1, 23, 25, 1, 25, 26, 1, 26, 28, 1, 28, 29, 1, 29, 31, 1, 31, 32, 1, 32, 34, 1, 34, 35, 1, 35, 37, 1
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OFFSET
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1,4
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COMMENTS
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This sequence is eventually quasilinear with period 6. Each component sequence has slope 0 or 1/2.
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LINKS
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FORMULA
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If the index is at least 41:
a(6n) = 1
a(6n+1) = 3n-1
a(6n+2) = 3n+1
a(6n+3) = 1
a(6n+4) = 3n+1
a(6n+5) = 3n+2.
G.f.: (-x^48-x^46-x^45-x^43+x^42+3*x^41+x^40-9*x^39-x^38+3*x^37+x^36-4*x^35+x^34+12*x^33+x^32-2*x^31+x^30+x^29-x^28+x^26-3*x^25-2*x^24-x^23+2*x^22-x^20+2*x^19+3*x^18-2*x^16-x^15+2*x^13-3*x^12+x^11-x^8+x^4+x^3+x^2+x+1) / ((1+x)*(1-x+x^2)*(-1+x)^2*(1+x+x^2)^2).
a(n) = a(n-3) + a(n-6) - a(n-9) for n > 49.
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MAPLE
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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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