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A190826 Number of permutations of 3 copies of 1..n introduced in order 1..n with no element equal to another within a distance of 1. 8
1, 0, 1, 29, 1721, 163386, 22831355, 4420321081, 1133879136649, 372419001449076, 152466248712342181, 76134462292157828285, 45552714996556390334921, 32173493282909179882613934, 26487410329744429030530295991, 25143126122564855343240882599761, 27260957330891104469298062949026065 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..223 (terms 0..101 from Andrew Woods)

H. Eriksson, A. Martin, Enumeration of Carlitz multipermutations, arXiv:1702.04177 (2017)

R. J. Mathar, A class of multinomial permutations avoiding object clusters, vixra:1511.0015 (2015), sequence M_{c,3}/3!.

FORMULA

Conjecture: 2*a(n) +3*(-3*n^2+3*n-4)*a(n-1) +2*(9*n^2-42*n+47)*a(n-2) +8*(3*n-7)*a(n-3) -8*a(n-4)=0. - R. J. Mathar, May 23 2014

a(n) ~ 3^(2*n + 1/2) * n^(2*n) / (2^n * exp(2*n + 2)). - Vaclav Kotesovec, Nov 24 2018

EXAMPLE

Some of the a(3) = 29 solutions for n=3: 123232131, 123121323, 123123213, 123212313, 123213123, 121323132, 123132312, 123123123, 123231213, 121323123, 121321323, 121312323, 121323231, 123231321, 121313232, 123132321,...

MATHEMATICA

a[n_] := 1/(6^n n!) Sum[(n+j)! Sum[Binomial[n, k] Binomial[2k, j] (-3)^(n + k - j), {k, Ceiling[j/2], n}], {j, 0, 2n}]; Array[a, 16] (* Jean-Fran├žois Alcover, Jul 22 2017, after Tani Akinari's code for A193638 *)

CROSSREFS

A193624(n) = a(n) * 6^n * n! for n>=1

A193638(n) = a(n) * n! for n>=1

A192990(n*(n+1)*(n+2)/6) = a(n) * 6^n * n! for n>=1

Row n=3 of A322013.

Sequence in context: A028478 A042627 A042624 * A045688 A084223 A138755

Adjacent sequences:  A190823 A190824 A190825 * A190827 A190828 A190829

KEYWORD

nonn

AUTHOR

R. H. Hardin, May 21 2011

EXTENSIONS

a(0)=1 prepended by Alois P. Heinz, Jul 22 2017

STATUS

approved

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Last modified December 6 16:24 EST 2019. Contains 329808 sequences. (Running on oeis4.)