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A116714
Number of permutations of length n that avoid the patterns 321, 1342, 4123.
1
1, 1, 2, 5, 12, 24, 46, 87, 162, 300, 554, 1021, 1880, 3460, 6366, 11711, 21542, 39624, 72882, 134053, 246564, 453504, 834126, 1534199, 2821834, 5190164, 9546202, 17558205, 32294576, 59398988, 109251774, 200945343, 369596110, 679793232, 1250334690, 2299724037
OFFSET
0,3
FORMULA
G.f.: (x^5 + 3*x^4 + x^3 - x+1)/((x-1)*(x^3 + x^2 + x - 1)).
MAPLE
A116714 := proc(n)
if n = 1 then
1;
else
-5+A000073(n+2)+4*A000073(n+1)+3*A000073(n) ;
%/2 ;
end if;
end proc:
seq(A116714(n), n=1..20) ; # R. J. Mathar, Jan 11 2024
MATHEMATICA
LinearRecurrence[{2, 0, 0, -1}, {1, 1, 2, 5, 12, 24}, 50] (* Paolo Xausa, Jan 19 2024 *)
CROSSREFS
Sequence in context: A192981 A116713 A261369 * A023615 A320235 A034483
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Feb 26 2006
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Jan 19 2024
STATUS
approved