A190918 Number of permutations of n copies of 1..4 introduced in order 1..4 with no element equal to another within a distance of 1.

1, 36, 1721, 94376, 5609649, 351574834, 22875971289, 1530622143864, 104650147201049, 7279277647839552, 513492654638478897, 36647810215955194122, 2641438793287744496337, 191996676519223794534702, 14057702378132873242943289, 1035863834231020871413190808

Offset: 1

Author

R. H. Hardin, May 23 2011

Keywords

• nonn

Examples

			Some solutions for n=2:
..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....3....3....3....3....3....3....1....3....3....1....3....3....3....1....3
..4....1....4....2....4....1....2....3....4....4....3....4....1....2....2....4
..2....4....1....4....1....4....4....4....2....2....4....3....4....4....3....2
..4....2....2....3....3....2....1....3....3....1....2....1....3....1....4....4
..3....3....4....1....4....4....3....4....4....4....3....4....4....4....3....1
..1....4....3....4....2....3....4....2....1....3....4....2....2....3....4....3
		

Links

• Richard Copley, Table of n, a(n) for n = 1..502 (first 106 terms from R. H. Hardin)
• R. J. Mathar, A class of multinomial permutations avoiding object clusters, vixra:1511.0015 (2015), sequence M_{4,m}/4!.

Crossrefs

Column k=4 of A322013.

Cf. A000012 (b=2), A190917 (b=3), A190920 (b=5), A190923 (b=6), A190927 (b=7), A190932 (b=8), A321987 (b=9).

Formula

Conjecture: n^3 *(n-1) *(2*n+1) *(5*n-7) *a(n) -2*(n-1) *(415*n^5 -1026*n^4 +727*n^3 -90*n^2 -98*n +36)*a(n-1) +(1630*n^4 -6387*n^3 +7388*n^2 +111*n -3510) *(n-2)^2 *a(n-2) -162*(3+5*n) *(n-2)^2 *(n-3)^3 *a(n-3)=0. - R. J. Mathar, Nov 01 2015

a(n) ~ 3^(4*n-2) / (Pi*n)^(3/2). - Vaclav Kotesovec, Nov 24 2018