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A240798
Total number of occurrences of the pattern 1=2=3 in all preferential arrangements (or ordered partitions) of n elements.
2
0, 0, 1, 12, 130, 1500, 18935, 262248, 3972612, 65500200, 1169398065, 22494463860, 464072915878, 10225330604580, 239720548513355, 5959152063448080, 156592569864940040, 4337574220496785680, 126329273251232688069, 3859509516112803668220, 123426111134706786806890
OFFSET
1,4
COMMENTS
There are A000670(n) preferential arrangements of n elements - see A000670, A240763.
The number that avoid the pattern 1=2=3 is given in A080599.
LINKS
FORMULA
a(n) ~ n! * n / (12 * (log(2))^(n-1)). - Vaclav Kotesovec, May 03 2015
MAPLE
b:= proc(n) option remember; `if`(n=0, [1, 0], add((p-> p+
[0, p[1]*binomial(j, 3)])(b(n-j))*binomial(n, j), j=1..n))
end:
a:= n-> b(n)[2]:
seq(a(n), n=1..25); # Alois P. Heinz, Dec 08 2014
MATHEMATICA
b[n_] := b[n] = If[n==0, {1, 0}, Sum[Function[p, p+{0, p[[1]]*Binomial[j, 3]} ][b[n-j]]*Binomial[n, j], {j, 1, n}]]; a[n_] := b[n][[2]]; Table[a[n], {n, 1, 25}] (* Jean-François Alcover, Feb 28 2017, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 13 2014
EXTENSIONS
a(8)-a(21) from Alois P. Heinz, Dec 08 2014
STATUS
approved