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A054668
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Number of distinct non-extendable sequences X={x(1),x(2),...,x(k)} where x(1)=1, the x(i)'s are distinct elements of {1,...,n} with |x(i)-x(i+1)|=1 or 2, for i=1,2,...,k.
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2
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1, 2, 4, 8, 16, 30, 56, 104, 192, 354, 652, 1200, 2208, 4062, 7472, 13744, 25280, 46498, 85524, 157304, 289328, 532158, 978792, 1800280, 3311232, 6090306, 11201820, 20603360, 37895488, 69700670, 128199520
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OFFSET
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1,2
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COMMENTS
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Superseeker suggests the g.f. ((x^4)+1)/(x^4-2x+1). If the sequences X, in the enumeration of a(n), are required to contain n then sequence A000073 (tribonacci numbers} is obtained.
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LINKS
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FORMULA
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a(1) = 1, a(n) = term (4,2) in the 4 X 4 matrix [1,1,0,0; 1,0,1,0; 1,0,0,0; 2,0,0,1]^n (n > 1). - Alois P. Heinz, Jul 24 2008
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EXAMPLE
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a(4) = 4, since the allowable sequences are {1,2,3,4}, {1,2,4,3}, {1,3,2,4} and {1,3,4,2}, whereas {1,4,2,3} and {1,4,3,2} violate the spacing condition.
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MAPLE
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a:= n-> `if`(n=1, 1, (<<1|1|0|0>, <1|0|1|0>, <1|0|0|0>, <2|0|0|1>>^n)[4, 2]):
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MATHEMATICA
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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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