A179958 -id:A179958 - cp's OEIS frontend

A127697 Number of permutations of {1,2,...,n} where adjacent elements differ in value by 3 or more.

1, 1, 0, 0, 0, 0, 2, 32, 368, 3984, 44304, 521606, 6564318, 88422296, 1272704694, 19521035238, 318120059458, 5491779703870, 100150978723568, 1924351621839740, 38864316540425434, 823161467837784388

Offset: 0

Richard Forster (gbrl01(AT)yahoo.co.uk), Apr 11 2007, Apr 26 2007

Equivalently, number of permutations of {1,2,...,n} where elements that differ by 1 in value are neither in positions i and i+1 (adjacent), nor i and i+2.

			Valid permutations of {1,...,6} are 415263 and 362514.

Robert P. P. McKone, The permutations n=6 to n=10.

Cf. A002464 (stride >= 2), A179957 (stride >= 4), A179958 (stride >=5).

Clear[permCount]; permCount[s_, last_] := permCount[s, last] = Module[{n, j}, n = Length[s]; If[n == 0, 1, Total[Table[If[Abs[last - j] >= 3, permCount[DeleteCases[s, j], j], 0], {j, s}]]]]; Table[permCount[Range[n], -2], {n, 0, 12}] (* Robert P. P. McKone, Mar 01 2025 *)

Jul 01 2010: Zak Seidov corrected a(10) and a(11). R. H. Hardin then computed a(12) through a(18).
Corrected first term to 1 (was 0).
a(0), a(19)-a(20) from Alois P. Heinz, Oct 27 2014
a(21) from Alois P. Heinz, Feb 09 2025

A249392 The number of down-up permutations of [n] where adjacent elements differ by at least 5.

Original entry on oeis.org

1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 32, 1088, 17280, 293832, 4004352, 57687080, 773838336, 10900027949, 151388845568, 2200665880514, 32321771402240, 495575856116168, 7760560549644288, 126552637539515688

Offset: 0

R. J. Mathar, Oct 27 2014

Cf. A245377 (at least 2), A249390 (at least 3), A249391 (at least 4), A249393 (at least 6), A179958 (non-alternating)

a(17)-a(21) from Alois P. Heinz, Oct 27 2014

a(22)-a(24) from Max Alekseyev, Feb 24 2024

A322308 Number of permutations sigma such that |sigma(i+j)-sigma(i)| >= 5 for 1 <= i <= n - j, 1 <= j <= 4.

Original entry on oeis.org

1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 128, 6320, 344872

Offset: 0

Seiichi Manyama, Dec 03 2018

2 | a(n) for n > 1.

			a(25) = 2: [5,10,15,20,25,4,9,14,19,24,3,8,13,18,23,2,7,12,17,22,1,6,11,16,21] and its reverse.

Cf. A179958, A279214, A322281.

cp's OEIS Frontend

A127697 Number of permutations of {1,2,...,n} where adjacent elements differ in value by 3 or more.

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A249392 The number of down-up permutations of [n] where adjacent elements differ by at least 5.

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Author

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Extensions

A322308 Number of permutations sigma such that |sigma(i+j)-sigma(i)| >= 5 for 1 <= i <= n - j, 1 <= j <= 4.

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