# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a226430 Showing 1-1 of 1 %I A226430 #21 Jul 22 2018 14:36:46 %S A226430 1,2,0,2,4,10,21,44,89,178,352,692,1355,2648,5171,10100,19744,38646, %T A226430 75761,148772,292653,576678,1138240,2250152,4454679,8830640,17525991, %U A226430 34820264,69244864,137815978,274487517,547035452,1090790465,2176043098,4342753696,8669805020,17313228899 %N A226430 The number of simple permutations of length n which avoid 1243 and 2431. %H A226430 Jay Pantone, The Enumeration of Permutations Avoiding 3124 and 4312, arXiv:1309.0832 [math.CO], (2013) %H A226430 Wikipedia, Permutation classes avoiding two patterns of length 4 %H A226430 Index entries for linear recurrences with constant coefficients, signature (4,-3,-4,3,2). %F A226430 G.f.: (x-2*x^2-5*x^3+12*x^4+x^5-8*x^6-3*x^7)/((1-2*x)*(1-x-x^2)^2). %F A226430 a(n) = -2*A000045(n+1) +A191830(n+2) +2^(n-3), n>2. - _R. J. Mathar_, Dec 06 2013 %t A226430 Join[{1, 2}, LinearRecurrence[{4, -3, -4, 3, 2}, {0, 2, 4, 10, 21}, 40]] (* _Jean-François Alcover_, Jul 22 2018 *) %o A226430 (PARI) x='x+O('x^66); Vec((x-2*x^2-5*x^3+12*x^4+x^5-8*x^6-3*x^7)/((1-2*x)*(1-x-x^2)^2)) \\ _Joerg Arndt_, Jun 19 2013 %Y A226430 The number of all permutations which avoid 1243 and 2431 is A165534. %K A226430 nonn %O A226430 1,2 %A A226430 _Jay Pantone_, Jun 06 2013 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE