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A227860
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Sequence of integers such that there are d terms between pairs of integers d. Cycle through d=0,1,2,3, trying to insert the least unused pair starting at the next free position.
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1
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0, 0, 1, 2, 1, 3, 2, 0, 0, 3, 1, 2, 1, 3, 2, 0, 0, 3, 1, 2, 1, 3, 2, 0, 0, 3, 1, 2, 1, 3, 2, 0, 0, 3, 1, 2, 1, 3, 2, 0, 0, 3, 1, 2, 1, 3, 2, 0, 0, 3, 1, 2, 1, 3, 2, 0, 0, 3, 1, 2, 1, 3, 2, 0, 0, 3, 1, 2, 1, 3, 2, 0, 0, 3, 1, 2, 1, 3, 2, 0, 0, 3
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OFFSET
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1,4
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COMMENTS
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After the two initial terms, the sequence enters the cycle (1,2,1,3,2,0,0,3) of length 8.
This is the lexicographically earliest (nontrivial) sequence of that type, with a range R={0,...,N}, following the example proposed by Eric Angelini (N=9: A227859), cf. link. Indeed, the ranges R={0,1} or R={0,1,2} are not possible. The range R={0,2} is also possible (cf. link).
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LINKS
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FORMULA
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a(n) = a(n-8) for n>10. G.f.: -x^3*(3*x^7+2*x^4+3*x^3+x^2+2*x+1) / ((x-1)*(x+1)*(x^2+1)*(x^4+1)). - Colin Barker, Nov 02 2013
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EXAMPLE
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Between a(1)=0 and a(2)=0 there are 0 other terms. Then one can place a(3)=1 and has to set a(5)=1 as to have 1 term in between these two. Then one can set a(4)=2=a(7). Then the next free position is a(6)=3=a(10), etc.
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PROG
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(PARI) Vec((3*x^9+2*x^6+3*x^5+x^4+2*x^3+x^2)/(-x^8+1) + O(x^100)) \\ Colin Barker, Nov 02 2013
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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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