cp's OEIS Frontend

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.

%I A190918 #30 Dec 12 2024 17:58:02
%S A190918 1,36,1721,94376,5609649,351574834,22875971289,1530622143864,
%T A190918 104650147201049,7279277647839552,513492654638478897,
%U A190918 36647810215955194122,2641438793287744496337,191996676519223794534702,14057702378132873242943289,1035863834231020871413190808
%N 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.
%H A190918 Richard Copley, <a href="/A190918/b190918.txt">Table of n, a(n) for n = 1..502</a> (first 106 terms from R. H. Hardin)
%H A190918 R. J. Mathar, <a href="http://vixra.org/abs/1511.0015">A class of multinomial permutations avoiding object clusters</a>, vixra:1511.0015 (2015), sequence M_{4,m}/4!.
%F A190918 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
%F A190918 a(n) ~ 3^(4*n-2) / (Pi*n)^(3/2). - _Vaclav Kotesovec_, Nov 24 2018
%e A190918 Some solutions for n=2:
%e A190918 ..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1
%e A190918 ..2....2....2....2....2....2....2....2....2....2....2....2....2....2....2....2
%e A190918 ..3....3....3....3....3....3....3....1....3....3....1....3....3....3....1....3
%e A190918 ..4....1....4....2....4....1....2....3....4....4....3....4....1....2....2....4
%e A190918 ..2....4....1....4....1....4....4....4....2....2....4....3....4....4....3....2
%e A190918 ..4....2....2....3....3....2....1....3....3....1....2....1....3....1....4....4
%e A190918 ..3....3....4....1....4....4....3....4....4....4....3....4....4....4....3....1
%e A190918 ..1....4....3....4....2....3....4....2....1....3....4....2....2....3....4....3
%Y A190918 Column k=4 of A322013.
%Y A190918 Cf. A000012 (b=2), A190917 (b=3), A190920 (b=5), A190923 (b=6), A190927 (b=7), A190932 (b=8), A321987 (b=9).
%K A190918 nonn
%O A190918 1,2
%A A190918 _R. H. Hardin_, May 23 2011