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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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
| 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, Jul 24 2008
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EXAMPLE
| 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
| 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, Jul 24 2008
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MATHEMATICA
| a=b=c=0; Join[{1}, Table[d=a+b+c+2; a=b; b=c; c=d, {n, 50}]] (* From Vladimir Joseph Stephan Orlovsky, Apr 19 2011 *)
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CROSSREFS
| Cf. A053623.
Sequence in context: A005305 A125548 A164229 * A164225 A164204 A164209
Adjacent sequences: A054665 A054666 A054667 * A054669 A054670 A054671
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KEYWORD
| nonn
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AUTHOR
| John W. Layman (layman(AT)math.vt.edu), Apr 18 2000
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