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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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19
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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
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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G.f.: (1 -x +x^2)/(1-2*x+x^2-x^3+x^4).
a(n) = a(n-1) + a(n-3) + 1. (End)
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MATHEMATICA
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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] (* Harvey P. Dale, Apr 24 2011 *)
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PROG
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(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -1, 1, -1, 2]^(n-1)*[1; 1; 2; 4])[1, 1] \\ Charles R Greathouse IV, Apr 07 2016
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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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EXTENSIONS
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STATUS
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approved
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