This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A164366 #28 Dec 17 2019 07:42:22 %S A164366 1,1,1,1,4,1,1,10,12,1,1,20,68,31,1,35,259,380,45,1,56,770,2700,1513, %T A164366 1,84,1932,13467,22000,2836,1,120,4284,52512,191636,114327,1,165,8646, %U A164366 170907,1183457,2010571,255053,1,220,16203,484440,5706464,21171518,12537954,1,286,28600,1231230,22822293,157499810,265819779,31599601,1,364,48048,2864719,78829491,910047453,3341572727,1893657570,427,1,455,77441,6196333,241943403,4334283646,29432517384,47916472532,5246800005 %N A164366 Triangle read by rows: T(n,k) is the number of permutations of n elements with transposition distance equal to k, n >= 1 and 0 <= k <= A065603(n). %C A164366 Here, a transposition refers to the exchange of two adjacent blocks, and NOT to an exchange of two nonnecessarily adjacent elements. The transposition distance is the minimum number of such moves required to transform a given permutation into the identity permutation. %D A164366 G. Fertin, A. Labarre, I. Rusu, E. Tannier, and S. Vialette, "Combinatorics of genome rearrangements", The MIT Press, 2009, page 26. %H A164366 V. Bafna and P. A. Pevzner, <a href="https://doi.org/10.1137/S089548019528280X">Sorting by transpositions</a>, SIAM Journal on Discrete Mathematics, 11 (1998), 224-240. %H A164366 V. Bafna and P. A. Pevzner, <a href="http://www.ic.unicamp.br/~meidanis/courses/mo640/2007s1/textos/Bafna-Pevzner-1998.pdf">Sorting by transpositions</a>, SIAM Journal on Discrete Mathematics, 11 (1998), 224-240. %H A164366 J. Gonçalves, L. R. Bueno, R. A. Hausen, <a href="https://pdfs.semanticscholar.org/b9df/0c38ed7fca7d5046513de19895412c9ff2c0.pdf">Assembling a New and Improved Transposition Distance Database</a>, in Simpósio Brasileiro de Pesquisa Operacional, Sept. 2013. %e A164366 The triangle of T(n,k) (with rows n >= 1 and columns k >= 0) starts as follows: %e A164366 1, %e A164366 1, 1, %e A164366 1, 4, 1, %e A164366 1, 10, 12, 1, %e A164366 1, 20, 68, 31, %e A164366 1, 35, 259, 380, 45, %e A164366 1, 56, 770, 2700, 1513, %e A164366 1, 84, 1932, 13467, 22000, 2836, %e A164366 1, 120, 4284, 52512, 191636, 114327, %e A164366 1, 165, 8646, 170907, 1183457, 2010571, 255053, %e A164366 ... %e A164366 The number of permutations of 4 elements with transposition distance 3 is 1, since only (4 3 2 1) cannot be sorted using fewer transpositions (upper bound can be easily found by hand; for the lower bound, see the paper by Bafna and Pevzner). %Y A164366 Cf. A219243 (main "diagonal"). See also A065603. %K A164366 nonn,tabf %O A164366 1,5 %A A164366 _Anthony Labarre_, Aug 14 2009 %E A164366 Edited by _Max Alekseyev_, Nov 07 2011 %E A164366 More terms from Gonçalves et al. added by _Max Alekseyev_, Nov 16 2012