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 A228394 The number of permutations of length n sortable by 2 prefix block transpositions. 0
 1, 2, 6, 21, 61, 146, 302, 561, 961, 1546, 2366, 3477, 4941, 6826, 9206, 12161, 15777, 20146, 25366, 31541, 38781, 47202, 56926, 68081, 80801, 95226, 111502, 129781, 150221, 172986, 198246, 226177, 256961, 290786, 327846, 368341, 412477, 460466, 512526, 568881 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Z. Dias and J. Meidanis, Sorting by prefix transpositions, In Proceedings of the 9th International Symposium on String Processing and Information Retrieval (London, UK, UK, 2002), SPIRE 2002, Springer-Verlag, pp. 65-76. C. Homberger, Patterns in Permutations and Involutions: A Structural and Enumerative Approach, arXiv preprint 1410.2657, 2014 C. Homberger, V. Vatter, On the effective and automatic enumeration of polynomial permutation classes, arXiv preprint arXiv:1308.4946, 2013 Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA G.f.: -1 -(x^2 + 1)*(6*x^2 - 4*x + 1)/(x - 1)^5. a(n) = 1 + (n-1)*n*(3*n^2-11*n+16)/12. [Bruno Berselli, Aug 22 2013] EXAMPLE There are 3 permutations of length 4 that cannot be sorted by 2 prefix block transpositions. MATHEMATICA CoefficientList[Series[(1/x) (-1 - (x^2 + 1) (6 x^2 - 4 x + 1)/(x - 1)^5), {x, 0, 50}], x] (* Bruno Berselli, Aug 22 2013 *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 2, 6, 21, 61}, 40] (* Harvey P. Dale, May 28 2018 *) CROSSREFS Cf. A000124, A228395. Sequence in context: A104143 A088812 A228398 * A245749 A001434 A119098 Adjacent sequences:  A228391 A228392 A228393 * A228395 A228396 A228397 KEYWORD nonn,easy AUTHOR Vincent Vatter, Aug 21 2013 STATUS approved

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Last modified April 21 10:03 EDT 2019. Contains 322328 sequences. (Running on oeis4.)