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Search: id:A054391
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| A054391 |
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Number of permutations with certain forbidden subsequences. |
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+0
5
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| 1, 1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997, 330632, 1032781, 3229714, 10109310, 31667245, 99260192, 311294876, 976709394, 3065676758, 9625674442, 30231524869, 94972205349, 298419158008, 937861780439, 2947969125284
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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E. Barcucci et al., From Motzkin to Catalan Permutations, Discr. Math., 217 (2000), 33-49.
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LINKS
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J. W. Layman, The Hankel Transform and Some of its Properties, J. Integer Sequences, 4 (2001), #01.1.5.
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MAPLE
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c := x->(1-sqrt(1-4*x))/(2*x); a := (x, j)->(x)/((1-4*x)*(c(x))^2*(1-c(x))^(j))*(-x^2*(c(x))^2*(1-c(x))*(x^2*(c(x))^4)^(j)-(1-3*x-2*x^2)*(c(x))^2*(x*(c(x))^2)^(j)+x);
b := (x, j)->1+(1)/((1-4*x)*c(x)*(1-c(x))^(j))*(-2*x^3*(c(x))^2*(x^2*(c(x))^4)^(j)+(1-3*x-2*x^2)*c(x)*(x*(c(x))^2)^(j)-2*x^2);
co := (x, j)->(1)/((1-4*x)*(1-c(x))^(j))*(x^2*(x^2*(c(x))^4)^(j)-(1-3*x-2*x^2)*(x*(c(x))^2)^(j)+x^2);
s := (x, j)->(1-b(x, j)+(-1)^j*sqrt((1-b(x, j))^2-4*a(x, j)*co(x, j)))/(2*a(x, j)); j := 3; series(s(x, j), x=0..60); od; # j=1, 2, 3, ... inf gives A001006, A005773, A054391, A054392, ..., A000108
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CROSSREFS
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Interpolates between Motzkin numbers (A001006) and Catalan numbers (A000108). Cf. A005773, A054392, ...
Sequence in context: A123183 A088355 A113485 this_sequence A108626 A128739 A036766
Adjacent sequences: A054388 A054389 A054390 this_sequence A054392 A054393 A054394
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KEYWORD
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nonn
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AUTHOR
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njas, Elisa Pergola (elisa(AT)dsi.unifi.it), May 21 2000
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