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 A228398 The number of permutations of length n sortable by 3 prefix reversals (in the pancake sorting sense). 0
 1, 2, 6, 21, 52, 105, 186, 301, 456, 657, 910, 1221, 1596, 2041, 2562, 3165, 3856, 4641, 5526, 6517, 7620, 8841, 10186, 11661, 13272, 15025, 16926, 18981, 21196, 23577, 26130, 28861, 31776, 34881, 38182, 41685, 45396, 49321, 53466, 57837, 62440, 67281, 72366 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Essentially the same as A069778. LINKS H. Dweighter, Elementary problems and solutions, problem E2569. Amer. Math. Monthly 82 (1975), 1010. 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. FORMULA G.f.: -1 + (x^6 - 3*x^5 + 6*x^4 + 4*x^2 - 3*x + 1)/(x - 1)^4. a(n) = (n-1)*(n^2-3*n+3) for n>2, a(1)=1, a(2)=2. [Bruno Berselli, Aug 22 2013] EXAMPLE There are only 3 permutations of length 4 which cannot be sorted by 3 pancake reversals. MATHEMATICA CoefficientList[Series[(1/x) (-1 + (x^6 - 3 x^5 + 6 x^4 + 4 x^2 - 3 x + 1)/(x - 1)^4), {x, 0, 50}], x] (* Bruno Berselli, Aug 22 2013 *) CROSSREFS Cf. A000027, A002522. Sequence in context: A004192 A104143 A088812 * A228394 A245749 A001434 Adjacent sequences:  A228395 A228396 A228397 * A228399 A228400 A228401 KEYWORD nonn,easy AUTHOR Vincent Vatter, Aug 21 2013 STATUS approved

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Last modified April 23 06:08 EDT 2019. Contains 322381 sequences. (Running on oeis4.)