The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A054394 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A054394

Number of permutations with certain forbidden subsequences.
(history; published version)

#17 by Bruno Berselli at Tue Oct 16 03:56:37 EDT 2018

STATUS

reviewed

approved

#16 by Michel Marcus at Tue Oct 16 00:20:40 EDT 2018

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proposed

reviewed

#15 by Michael De Vlieger at Mon Oct 15 16:47:35 EDT 2018

STATUS

editing

proposed

#14 by Michael De Vlieger at Mon Oct 15 16:47:34 EDT 2018

LINKS

Nickolas Hein, Jia Huang, <a href="https://arxiv.org/abs/1807.04623">Nonassociativity measurements Variations of the Catalan numbers from some nonassociative binary operations</a>, arXiv:1807.04623 [math.CO], 2018.

STATUS

approved

editing

#13 by Susanna Cuyler at Thu Aug 16 13:24:39 EDT 2018

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proposed

approved

#12 by Jean-François Alcover at Thu Aug 16 09:24:14 EDT 2018

STATUS

editing

proposed

#11 by Jean-François Alcover at Thu Aug 16 09:24:10 EDT 2018

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-François Alcover, Aug 16 2018, after A054391 *)

STATUS

approved

editing

#10 by Bruno Berselli at Fri Jul 13 04:08:21 EDT 2018

STATUS

proposed

approved

#9 by Michel Marcus at Fri Jul 13 00:43:58 EDT 2018

STATUS

editing

proposed

#8 by Michel Marcus at Fri Jul 13 00:43:54 EDT 2018

REFERENCES

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

LINKS

E. Barcucci et al., <a href="http://dx.doi.org/10.1016/S0012-365X(99)00254-X">From Motzkin to Catalan Permutations</a>, Discr. Math., 217 (2000), 33-49.

Nickolas Hein, Jia Huang, <a href="https://arxiv.org/abs/1807.04623">Nonassociativity measurements of some binary operations</a>, 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. [From __R. J. Mathar_, Jul 07 2009]

STATUS

approved

editing