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A054394 Number of permutations with certain forbidden subsequences. 2
1, 1, 2, 5, 14, 42, 132, 429, 1429, 4847, 16660, 57820, 202086, 709928, 2503266, 8850681, 31355020, 111242127, 395091069, 1404332528, 4994581900, 17771328588, 63253477326, 225194224134, 801884971816, 2855809269782, 10171707099565 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..26.

E. Barcucci et al., From Motzkin to Catalan Permutations, Discr. Math., 217 (2000), 33-49.

Nickolas Hein, Jia Huang, Variations of the Catalan numbers from some nonassociative binary operations, arXiv:1807.04623 [math.CO], 2018.

FORMULA

Conjecture: g.f.(x)=1+z*(1-2z+z^2-z^3)/(1-3z+3z^2-3z^3+2z^4-z^5) where z=x*A001006(x) and A001006(x) is the g.f. of A001006. [R. J. Mathar, Jul 07 2009]

MATHEMATICA

a[0] = 1; a[n_] := Module[{M}, M = Table[If[j < i || i == j && i <= 6 || j == i+1, 1, 0], {i, 1, n}, {j, 1, n}]; MatrixPower[M, n][[1, 1]]];

Table[a[n], {n, 0, 26}] (* Jean-Fran├žois Alcover, Aug 16 2018, after A054391 *)

CROSSREFS

Interpolates between Motzkin numbers (A001006) and Catalan numbers (A000108). Cf. A005773, A054391-A054393.

Sequence in context: A287970 A058094 A080938 * A261590 A036769 A287971

Adjacent sequences:  A054391 A054392 A054393 * A054395 A054396 A054397

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Elisa Pergola (elisa(AT)dsi.unifi.it), May 21 2000

STATUS

approved

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Last modified February 22 15:52 EST 2019. Contains 320399 sequences. (Running on oeis4.)