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A060158
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Number of permutations of [n] with 4 sequences.
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4
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0, 0, 0, 0, 0, 32, 300, 1852, 9576, 45096, 201060, 866324, 3650592, 15154240, 62260380, 253939116, 1030367448, 4165106264, 16790875860, 67553807428, 271383782544, 1089035545968, 4366631897100, 17497971562460, 70086163646280, 280627369334152, 1123357369925700
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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REFERENCES
| L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 261.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,200
E. Rodney Canfield and Herbert S. Wilf, Counting permutations by their runs up and down [See u_4.]
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FORMULA
| a(n) = 2n-7+(6-n)2^(n-1)-3^n+4^(n-1).
G.f.: 4*x^5*(8-29*x+24*x^2)/((1-4*x)*(1-3*x)*(1-2*x)^2*(1-x)^2).
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MAPLE
| n4 := n->2*n-7+(6-n)*2^(n-1)-3^n+4^(n-1); seq(n4(i), i=5..27);
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PROG
| (PARI) { for (n=0, 200, if (n<2, a=0, a=2*n - 7 + (6 - n)*2^(n - 1) - 3^n + 4^(n - 1)); write("b060158.txt", n, " ", a); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 02 2009]
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CROSSREFS
| Cf. A028399, A060157, A000486, A059427, A000352, A123003.
Sequence in context: A122103 A009526 A197523 * A074469 A159654 A061958
Adjacent sequences: A060155 A060156 A060157 * A060159 A060160 A060161
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KEYWORD
| nonn
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AUTHOR
| Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 3/12/01
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 11 2006
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