The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A323671

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A323671

Number T(n,k) of permutations p of [n] with no fixed points such that |{ j : |p(j)-j| = 1 }| = k; triangle T(n,k), n >= 0, 0 <= k <= n, read by rows.
(history; published version)

#24 by Alois P. Heinz at Tue Feb 09 08:19:34 EST 2021

STATUS

proposed

approved

#23 by Jean-Fran�ois Alcover at Tue Feb 09 07:39:26 EST 2021

STATUS

editing

proposed

#22 by Jean-Fran�ois Alcover at Tue Feb 09 07:39:21 EST 2021

MATHEMATICA

b[s_] := b[s] = Expand[Function[n, If[n==0, 1, Sum[Function[t, If[t==0, 0, If[t==1, x, 1]*b[s~Complement~{j}]]][Abs[n-j]], {j, s}]]][Length[s]]];

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

T /@ Range[0, 12] // Flatten (* Jean-Fran�ois Alcover, Feb 09 2021, after Alois P. Heinz *)

STATUS

approved

editing

#21 by Alois P. Heinz at Fri Mar 01 16:02:43 EST 2019

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editing

approved

#20 by Alois P. Heinz at Fri Mar 01 16:02:41 EST 2019

EXAMPLE

...

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approved

editing

#19 by Alois P. Heinz at Wed Jan 23 18:04:28 EST 2019

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editing

approved

#18 by Alois P. Heinz at Wed Jan 23 18:04:25 EST 2019

CROSSREFS

Cf. A296050, A320582, A323664.

STATUS

approved

editing

#17 by Alois P. Heinz at Wed Jan 23 17:56:18 EST 2019

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editing

approved

#16 by Alois P. Heinz at Wed Jan 23 17:56:16 EST 2019

FORMULA

Sum_{k=1..n} T(n,k) = A296050(n).

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approved

editing

#15 by Alois P. Heinz at Wed Jan 23 17:51:01 EST 2019

STATUS

editing

approved