The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A343535 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A343535

Number T(n,k) of permutations of [n] having exactly k consecutive triples j, j+1, j-1; triangle T(n,k), n>=0, 0<=k<=floor(n/3), read by rows.
(history; published version)

#25 by Michel Marcus at Mon Apr 26 08:53:52 EDT 2021

STATUS

reviewed

approved

#24 by Joerg Arndt at Mon Apr 26 08:01:06 EDT 2021

STATUS

proposed

reviewed

#23 by Jean-François Alcover at Mon Apr 26 07:21:09 EDT 2021

STATUS

editing

proposed

#22 by Jean-François Alcover at Mon Apr 26 07:21:05 EDT 2021

MATHEMATICA

b[s_, l_, t_] := b[s, l, t] = If[s == {}, 1, Sum[Function[h,

Expand[b[s ~Complement~ {j}, j, If[h == 1, 2, 1]]*

If[t == 2 && h == -2, x, 1]]][j - l], {j, s}]];

T[n_] := CoefficientList[b[Range[n], -1, 1], x];

T /@ Range[0, 13] // Flatten (* Jean-François Alcover, Apr 26 2021, after Alois P. Heinz *)

STATUS

approved

editing

#21 by Alois P. Heinz at Wed Apr 21 16:50:11 EDT 2021

STATUS

editing

approved

#20 by Alois P. Heinz at Wed Apr 21 08:48:09 EDT 2021

CROSSREFS

Cf. A047921, A123513, A197365, A216716.

STATUS

approved

editing

#19 by Alois P. Heinz at Tue Apr 20 16:53:23 EDT 2021

STATUS

editing

approved

#18 by Alois P. Heinz at Tue Apr 20 12:55:06 EDT 2021

CROSSREFS

Cf. A047921, A123513, A197365.

STATUS

approved

editing

#17 by Alois P. Heinz at Mon Apr 19 11:25:51 EDT 2021

STATUS

editing

approved

#16 by Alois P. Heinz at Mon Apr 19 11:25:23 EDT 2021

LINKS

Anders Claesson, <a href="https://akc.is/papers/036-From-Hertzsprungs-problem-to-pattern-rewriting-systems.pdf">From Hertzsprung's problem to pattern-rewriting systems</a>, University of Iceland (2020).