A190830 Number of permutations of 4 copies of 1..n introduced in order 1..n with no element equal to another within a distance of 1.

1, 0, 1, 182, 94376, 98371884, 182502973885, 551248360550999, 2536823683737613858, 16904301142107043464659, 156690501089429126239232946, 1955972150994131850032960933480, 32016987304767134806200915633253966, 672058204939482014438623912695190927357

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..158 (terms 1..28 from R. J. Mathar)

R. J. Mathar, A class of multinomial permutations avoiding object clusters, vixra:1511.0015 (2015), sequence M_{c,4}/c!.

Formula

From Vaclav Kotesovec, Nov 24 2018: (Start)

Recurrence: 3*(64*n^3 - 280*n^2 + 414*n - 245)*a(n) = (2048*n^6 - 12032*n^5 + 30400*n^4 - 42608*n^3 + 32484*n^2 - 14624*n + 1731)*a(n-1) + 3*(3840*n^5 - 20640*n^4 + 40104*n^3 - 36340*n^2 + 23378*n - 13429)*a(n-2) - 18*(384*n^4 - 1488*n^3 + 1556*n^2 - 986*n + 649)*a(n-3) - 27*(64*n^3 - 88*n^2 + 46*n - 47)*a(n-4).

a(n) ~ 2^(5*n+1) * n^(3*n) / (3^n * exp(3*n + 3)). (End)

Example

Some solutions for n=3:
  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2
  3  1  3  3  1  3  3  3  3  3  3  1  1  3  1  1
  1  2  2  2  2  2  2  1  1  2  1  3  3  1  3  2
  2  3  3  3  1  1  3  2  2  3  2  1  2  3  1  1
  3  2  1  2  3  2  1  3  1  1  3  2  3  2  2  3
  1  3  2  3  2  3  3  1  3  2  2  3  2  1  3  1
  3  2  3  1  3  1  2  3  1  1  1  2  1  3  2  3
  1  1  1  3  1  3  1  2  2  3  3  3  2  2  3  2
  2  3  2  1  3  2  3  1  3  1  1  2  3  3  1  3
  3  1  1  2  2  3  1  3  2  2  2  3  1  1  3  2
  2  3  3  1  3  1  2  2  3  3  3  1  3  2  2  3

Crossrefs

Row n=4 of A322013.

Cf. A190826, A321633.

Sequence in context: A048546 A225712 A015306 * A145525 A028676 A228535

Adjacent sequences: A190827 A190828 A190829 * A190831 A190832 A190833

Keyword

nonn

Author

R. H. Hardin, May 21 2011

Extensions

a(0)=1 prepended by Seiichi Manyama, Nov 16 2018

Status

approved