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A190826
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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.
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8
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1, 0, 1, 29, 1721, 163386, 22831355, 4420321081, 1133879136649, 372419001449076, 152466248712342181, 76134462292157828285, 45552714996556390334921, 32173493282909179882613934, 26487410329744429030530295991, 25143126122564855343240882599761, 27260957330891104469298062949026065
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OFFSET
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0,4
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LINKS
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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!.
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FORMULA
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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
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EXAMPLE
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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,...
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MATHEMATICA
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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-François Alcover, Jul 22 2017, after Tani Akinari's code for A193638 *)
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, May 21 2011
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EXTENSIONS
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a(0)=1 prepended by Alois P. Heinz, Jul 22 2017
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STATUS
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approved
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