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A038718
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Number of permutations P of {1,2,...,n} such that P(1)=1 and |P^-1(i+1)-P^-1(i)| equals 1 or 2 for i=1,2,...,n-1.
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3
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1, 1, 2, 4, 6, 9, 14, 21, 31, 46, 68, 100, 147, 216, 317, 465, 682, 1000, 1466, 2149, 3150, 4617, 6767, 9918, 14536, 21304, 31223, 45760, 67065, 98289, 144050, 211116, 309406, 453457, 664574, 973981, 1427439, 2092014, 3065996, 4493436, 6585451
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| This sequence is the number of digits of each term of A061583. [From Dmitry Kamenetsky (dkamen(AT)rsise.anu.edu.au), Jan 17 2009]
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FORMULA
| G.f.: (x^2-x+1)/(x^4-x^3+x^2-2x+1). a(n) = a(n-1) + a(n-3) + 1. - Joseph Myers (jsm(AT)polyomino.org.uk), Feb 03 2004
a(n) = sum_{i=1..n} A058278(i) = A097333(n)-1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 16 2010]
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MATHEMATICA
| Join[{a=1, b=1, c=2}, Table[d=a+c+1; a=b; b=c; c=d, {n, 100}]] (*From Vladimir Joseph Stephan Orlovsky, Feb 26 2011*)
LinearRecurrence[{2, -1, 1, -1}, {1, 1, 2, 4}, 50] (* or *) CoefficientList[ Series[(x^2-x+1)/(x^4-x^3+x^2-2x+1), {x, 0, 50}], x] (* From Harvey P. Dale, Apr 24 2011 *)
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CROSSREFS
| Cf. A003274.
Cf. A003410.
Sequence in context: A139135 A097197 A119737 * A042942 A005687 A164139
Adjacent sequences: A038715 A038716 A038717 * A038719 A038720 A038721
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KEYWORD
| nonn
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AUTHOR
| John W. Layman (layman(AT)math.vt.edu), May 02 2000
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EXTENSIONS
| More terms from Joseph Myers (jsm(AT)polyomino.org.uk), Feb 03 2004
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