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 A228393 The number of permutations of length n that can be sorted by 3 block transpositions. 1
 1, 2, 6, 24, 120, 675, 3527, 15484, 56917, 179719, 500864, 1260117, 2913132, 6274230, 12726573, 24521243, 45190897, 80108200, 137224138, 228026582, 368765112, 581994117, 898492563, 1359625566, 2020220021, 2952034021, 4247907652, 6026690971, 8439053564 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..29. V. Bafna and P.A. Pevzner, Sorting by transpositions, SIAM J. Discrete Math. 11, 2 (1998), 224-240. Cheyne Homberger, Patterns in Permutations and Involutions: A Structural and Enumerative Approach, arXiv:1410.2657 [math.CO], 2014. C. Homberger, V. Vatter, On the effective and automatic enumeration of polynomial permutation classes, arXiv:1308.4946 [math.CO], 2013. Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1). FORMULA G.f.: -x*(x^9 - 9*x^8 - 17*x^7 - 263*x^6 - 3*x^5 - 120*x^4 + 66*x^3 - 31*x^2 + 8*x - 1)/(x - 1)^10. EXAMPLE The shortest permutations which cannot be sorted by 3 block transpositions are of length 6. MATHEMATICA CoefficientList[Series[-(x^9 - 9 x^8 - 17 x^7 - 263 x^6 - 3 x^5 - 120 x^4 + 66 x^3 - 31 x^2 + 8 x - 1)/(x - 1)^10, {x, 0, 40}], x] (* Bruno Berselli, Aug 22 2013 *) CROSSREFS Cf. A000292, A228392. Sequence in context: A152344 A152340 A152347 * A177526 A214611 A177528 Adjacent sequences: A228390 A228391 A228392 * A228394 A228395 A228396 KEYWORD nonn,easy AUTHOR Vincent Vatter, Aug 21 2013 STATUS approved

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Last modified September 21 17:55 EDT 2023. Contains 365503 sequences. (Running on oeis4.)