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 A163824 Number of permutations of length n in the 2x2 double-chevron permutation grid class. 0
 1, 1, 2, 6, 24, 106, 470, 2038, 8624, 35754, 145902, 588358, 2351910, 9341814, 36936146, 145567966, 572415344, 2247578314, 8816986046, 34570684966, 135522530174, 531285354214, 2083180354466, 8170672802686, 32059325714054, 125845764142006, 494223989283650 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The double-chevron grid class is the monotone grid class of permutations Grid((1,1),(-1,-1)). LINKS Table of n, a(n) for n=0..26. David Bevan, Permutation Grid Classes FORMULA O.g.f: 1/sqrt(1-4*x) - x*(1-x)/((1-2*x)*(1-3*x)). a(n) = A000984(n) - A027649(n-1). Conjecture: n*(n^2-6*n+11)*a(n) +(-9*n^3+56*n^2-119*n+60)*a(n-1) +2*(13*n^3-83*n^2+193*n-150)*a(n-2) -12*(2*n-5)*(n^2-4*n+6)*a(n-3) =0 . - R. J. Mathar, Jul 24 2012 EXAMPLE a(5) = 106 because the following 14 permutations can't be gridded (and hence are in the basis of the permutation class): 12543, 13254, 14253, 15243, 15423, 25413, 31254, 35412, 41253, 51243, 51423, 52413, 53412, 54123. MATHEMATICA CoefficientList[Series[1/Sqrt[1-4x]-(x(1-x))/((1-2x)(1-3x)), {x, 0, 30}], x] (* Harvey P. Dale, Jun 09 2016 *) CROSSREFS Sequence in context: A337770 A171338 A327006 * A356782 A094433 A178594 Adjacent sequences: A163821 A163822 A163823 * A163825 A163826 A163827 KEYWORD nonn AUTHOR David Bevan, Jun 27 2012 STATUS approved

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Last modified September 15 19:17 EDT 2024. Contains 375954 sequences. (Running on oeis4.)