The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A174080 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A174080

Number of permutations of length n with no consecutive triples i,i+d,i+2d for all d>0.
(history; published version)

#16 by Alois P. Heinz at Tue Sep 27 07:56:01 EDT 2022

STATUS

proposed

approved

#15 by Jean-François Alcover at Tue Sep 27 07:25:57 EDT 2022

STATUS

editing

proposed

#14 by Jean-François Alcover at Tue Sep 27 07:25:51 EDT 2022

MATHEMATICA

b[s_, x_, y_] := b[s, x, y] = If[s == {}, 1, Sum[If[x == 0 || x < y || x-y != y-j, b[s~Complement~{j}, y, j], 0], {j, s}]];

a[n_] := b[Range[n], 0, 0];

Table[a[n], {n, 0, 14}] (* Jean-François Alcover, Sep 27 2022, after Alois P. Heinz *)

STATUS

approved

editing

#13 by Alois P. Heinz at Sat Apr 17 22:18:10 EDT 2021

STATUS

editing

approved

#12 by Alois P. Heinz at Sat Apr 17 22:18:02 EDT 2021

DATA

1, 1, 2, 5, 21, 100, 597, 4113, 32842, 292379, 2925367, 31983248, 383514347, 4966286235, 69508102006, 1039315462467, 16627618496319, 282023014602100, 5075216962675445, 96263599713301975, 1925002914124917950

EXTENSIONS

a(0)-a(3) and a(10)-a(1920) from Alois P. Heinz, Apr 13 2021

STATUS

approved

editing

#11 by Alois P. Heinz at Tue Apr 13 19:41:55 EDT 2021

STATUS

editing

approved

#10 by Alois P. Heinz at Tue Apr 13 18:29:25 EDT 2021

MAPLE

b:= proc(s, x, y) option remember; `if`(s={}, 1, add(

`if`(x=0 or x<y or x-y<>y-j,

b(s minus {j}, y, j), 0), j=s))

end:

a:= n-> b({$1..n}, 0$2):

seq(a(n), n=0..14); # Alois P. Heinz, Apr 13 2021

#9 by Alois P. Heinz at Tue Apr 13 18:23:52 EDT 2021

DATA

1, 1, 2, 5, 21, 100, 597, 4113, 32842, 292379, 2925367, 31983248, 383514347, 4966286235, 69508102006, 1039315462467, 16627618496319, 282023014602100, 5075216962675445, 96263599713301975

EXTENSIONS

a(0)-a(3) and a(10)-a(1819) from Alois P. Heinz, Apr 13 2021

#8 by Alois P. Heinz at Tue Apr 13 17:41:31 EDT 2021

CROSSREFS

Cf. A002628, A174072, A174081, A174082, A174083, A295370.

#7 by Alois P. Heinz at Tue Apr 13 17:39:11 EDT 2021

DATA

1, 1, 2, 5, 21, 100, 597, 4113, 32842, 292379, 2925367, 31983248, 383514347, 4966286235, 69508102006, 1039315462467, 16627618496319, 282023014602100, 5075216962675445

EXTENSIONS

a(0)-a(3) and a(10)-a(1618) from Alois P. Heinz, Apr 13 2021