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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Paolo Xausa, Table of n, a(n) for n = 0..1000 Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005. Index entries for linear recurrences with constant coefficients, signature (2,0,0,-1). 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 Adjacent sequences: A116711 A116712 A116713 * A116715 A116716 A116717 KEYWORD nonn,easy AUTHOR Lara Pudwell, Feb 26 2006 EXTENSIONS a(0)=1 prepended by Alois P. Heinz, Jan 19 2024 STATUS approved

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Last modified September 18 20:35 EDT 2024. Contains 376002 sequences. (Running on oeis4.)