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 A061552 Number of 1324-avoiding permutations of length n. 12
 1, 1, 2, 6, 23, 103, 513, 2762, 15793, 94776, 591950, 3824112, 25431452, 173453058, 1209639642, 8604450011, 62300851632, 458374397312, 3421888118907, 25887131596018, 198244731603623, 1535346218316422, 12015325816028313, 94944352095728825, 757046484552152932, 6087537591051072864 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES Bóna, M.: Combinatorics of Permutations. Discrete Mathematics and its Applications (Boca Raton), 2nd edn. CRC Press, Boca Raton (2012) LINKS David Bevan, Table of n, a(n) for n = 0..50 (from the Conway/Guttmann reference; terms 0..31 by Joerg Arndt, taken from the Johansson/Nakamura reference; terms 37..50 by Bjarki Ágúst Guðmundsson, taken from the Conway/Guttmann/Zinn-Justin reference). M. H. Albert, M. Elder, A. Rechnitzer, P. Westcott, M. Zabrocki, On the Wilf-Stanley limit of 4231-avoiding permutations and a conjecture of Arratia, arXiv:math.CO/0502504, 2005. R. Arratia, On the Stanley-Wilf conjecture for the number of permutations avoiding a given pattern. Electron. J. Combin. 6, N1 (1999). D. Bevan, Permutations avoiding 1324 and patterns in Łukasiewicz paths, arXiv:1406.2890 [math.CO], 2014-2015. Miklós Bóna, A new upper bound for 1324-avoiding permutations, arXiv:1207.2379 [math.CO], 2012. Miklós Bóna, A new upper bound for 1324-avoiding permutations, Combin. Probab. Comput. 23(5), 717-724 (2014). Miklós Bóna, A new record for 1324-avoiding permutations, arXiv:1404.4033 [math.CO], 2014. Miklós Bóna, A new record for 1324-avoiding permutations, European Journal of Mathematics (2015) 1:198-206, DOI 10.1007/s40879-014-0020-6. A. Claesson, V. Jelínek, and E. Steingrímsson, Upper bounds for the Stanley-Wilf limit of 1324 and other layered patterns. J. Combin. Theory Ser. A 119(8), 1680-1691 (2012). Andrew R. Conway and Anthony J. Guttmann, On the growth rate of 1324-avoiding permutations, arXiv:1405.6802 [math.CO], (2014). Andrew R. Conway, Anthony J. Guttmann and Paul Zinn-Justin, 1324-avoiding permutations revisited, arXiv preprint arXiv:1709.01248 [math.CO], 2017. Steven Finch, Pattern-Avoiding Permutations [Broken link?] Steven Finch, Pattern-Avoiding Permutations [Cached copy, with permission] A. L. L. Gao, S. Kitaev, P. B. Zhang. On pattern avoiding indecomposable permutations, arXiv:1605.05490 [math.CO], 2016. Fredrik Johansson and Brian Nakamura, Using functional equations to enumerate 1324-avoiding permutations, arXiv:1309.7117 [math.CO], (2013). A. Marcus and G. Tardos, Excluded permutation matrices and the Stanley-Wilf conjecture, J. Combin. Theory Ser. A 107(1), 153-160 (2004). B. K. Nakamura, Computational methods in permutation patterns, PhD Dissertation, Rutgers University, May 2013. Brian Nakamura and Doron Zeilberger, Using Noonan-Zeilberger Functional Equations to enumerate (in Polynomial Time!) Generalized Wilf classes, arXiv preprint arXiv:1209.2353 [math.CO], 2012. Anthony Zaleski, Doron Zeilberger, On the Intriguing Problem of Counting (n+1,n+2)-Core Partitions into Odd Parts, arXiv:1712.10072 [math.CO], 2017. EXAMPLE a(4)=23 because all 24 permutations of length 4, except 1324 itself, avoid the pattern 1324. MAPLE count1324 := proc(n::nonnegint) if (n<4) then return n!; fi; if (n=4) then return 23; fi; return nodes([5, 5, 5, 5], n-5) + nodes([5, 3, 5, 5], n-5) + nodes([5, 4, 4, 5], n-5) + nodes([5, 5, 4, 5], n-5) + nodes([4, 3, 4], n-5) + nodes([5, 3, 4, 5], n-5); end: nodes := proc(p, h) option remember; local i, j, s, l; if (h=0) then return convert(p, `+`); fi; s := 0; for j to nops(p) do l := p[j]+1; for i from 2 to j do l := l, `min`(j+1, p[i]); od; for i from j+1 to p[j] do l := l, p[i-1]+1; od; s := s+nodes([l], h-1); od; return s; end: MATHEMATICA a[n_] := n!/; n<4; a[4]=23; a[n_] := Total[nodes[#, n-5]&/@{{4, 3, 4}, {5, 3, 4, 5}, {5, 3, 5, 5}, {5, 4, 4, 5}, {5, 5, 4, 5}, {5, 5, 5, 5}}]; nodes[p_, 0]:=Total[p]; nodes[p_, h_] := nodes[p, h] = Sum[nodes[Join[{p[[j]]+1}, Min[j+1, #]&/@p[[2;; j]], p[[j;; p[[j]]-1]]+1], h-1], {j, Length[p]}]; Array[a, 12] (* David Bevan, May 25 2012 *) CROSSREFS A005802, A022558, A061552 are representatives for the three Wilf classes for length-four avoiding permutations (cf. A099952). Sequence in context: A004040 A216040 A005802 * A263778 A053488 A117106 Adjacent sequences:  A061549 A061550 A061551 * A061553 A061554 A061555 KEYWORD nonn AUTHOR Darko Marinov (marinov(AT)lcs.mit.edu), May 17 2001 EXTENSIONS More terms from Vincent Vatter, Feb 26 2005 a(23)-a(25) added from the Albert et al. paper by N. J. A. Sloane, Mar 29 2013 STATUS approved

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Last modified December 9 17:51 EST 2018. Contains 318023 sequences. (Running on oeis4.)