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Search: id:A054668
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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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+0
3
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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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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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FORMULA
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a(1) = 1, a(n) = term (4,2) in the 4x4 matrix [1,1,0,0; 1,0,1,0; 1,0,0,0; 2,0,0,1]^n (n>1). - Alois P. Heinz (heinz(AT)hs-heilbronn.de), 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 then 1 else (Matrix ([[1, 1, 0, 0], [1, 0, 1, 0], [1, 0, 0, 0], [2, 0, 0, 1]])^n)[4, 2] fi; seq (a(n), n=1..50); - Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 24 2008
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CROSSREFS
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Cf. A053623.
Sequence in context: A005305 A125548 A164229 this_sequence A164225 A164204 A164209
Adjacent sequences: A054665 A054666 A054667 this_sequence A054669 A054670 A054671
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Apr 18 2000
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