A190830 - OEIS

%I #31 Nov 25 2018 04:58:40

%S 1,0,1,182,94376,98371884,182502973885,551248360550999,

%T 2536823683737613858,16904301142107043464659,

%U 156690501089429126239232946,1955972150994131850032960933480,32016987304767134806200915633253966,672058204939482014438623912695190927357

%N 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.

%H Seiichi Manyama, <a href="/A190830/b190830.txt">Table of n, a(n) for n = 0..158</a> (terms 1..28 from R. J. Mathar)

%H 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_{c,4}/c!.

%F From _Vaclav Kotesovec_, Nov 24 2018: (Start)

%F 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).

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

%e Some solutions for n=3:

%e   1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1

%e   2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2

%e   3  1  3  3  1  3  3  3  3  3  3  1  1  3  1  1

%e   1  2  2  2  2  2  2  1  1  2  1  3  3  1  3  2

%e   2  3  3  3  1  1  3  2  2  3  2  1  2  3  1  1

%e   3  2  1  2  3  2  1  3  1  1  3  2  3  2  2  3

%e   1  3  2  3  2  3  3  1  3  2  2  3  2  1  3  1

%e   3  2  3  1  3  1  2  3  1  1  1  2  1  3  2  3

%e   1  1  1  3  1  3  1  2  2  3  3  3  2  2  3  2

%e   2  3  2  1  3  2  3  1  3  1  1  2  3  3  1  3

%e   3  1  1  2  2  3  1  3  2  2  2  3  1  1  3  2

%e   2  3  3  1  3  1  2  2  3  3  3  1  3  2  2  3

%Y Row n=4 of A322013.

%Y Cf. A190826, A321633.

%K nonn

%O 0,4

%A _R. H. Hardin_, May 21 2011

%E a(0)=1 prepended by _Seiichi Manyama_, Nov 16 2018