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A324375 Number of permutations p of [n] whose absolute displacements |p(i)-i| are square numbers. 4
1, 1, 2, 3, 5, 13, 29, 68, 165, 339, 1249, 3706, 11749, 39151, 105714, 321361, 938529, 4112583, 16778058, 64073812, 260625900, 917269164, 3451696842, 13068376545, 48655092849 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..24.

Wikipedia, Permutation

EXAMPLE

a(3) = 3: 123, 132, 213.

a(4) = 5: 1234, 1243, 1324, 2134, 2143.

a(5) = 13: 12345, 12354, 12435, 13245, 13254, 21345, 21354, 21435, 23451, 51234, 52341, 52431, 53241.

MAPLE

b:= proc(s) option remember; (n-> `if`(n=0, 1, add(`if`(

     issqr(abs(n-j)), b(s minus {j}), 0), j=s)))(nops(s))

    end:

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

seq(a(n), n=0..16);

MATHEMATICA

b[s_] := b[s] = Function[n, If[n == 0, 1, Sum[If[IntegerQ@Sqrt[Abs[n-j]], b[s ~Complement~ {j}], 0], {j, s}]]][Length[s]];

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

a /@ Range[0, 16] (* Jean-Fran├žois Alcover, Apr 23 2021, after Alois P. Heinz *)

CROSSREFS

Cf. A000142, A000290, A324372, A324373, A324374, A324376.

Sequence in context: A072536 A087592 A248526 * A038879 A162390 A108515

Adjacent sequences:  A324372 A324373 A324374 * A324376 A324377 A324378

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 25 2019

STATUS

approved

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Last modified August 9 15:33 EDT 2022. Contains 356026 sequences. (Running on oeis4.)