A060158 Number of permutations of [n] with 4 sequences.

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

Offset: 0

Author

Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Mar 12 2001

Keywords

• nonn

References

• L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 261.

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, arXiv:math/0609704 [math.CO], 2006. [See u_4.]
• Index entries for linear recurrences with constant coefficients, signature (13, -67, 175, -244, 172, -48).

Crossrefs

Cf. A028399, A060157, A000486, A059427, A000352, A123003.

Programs

Maple

n4 := n->2*n-7+(6-n)*2^(n-1)-3^n+4^(n-1); seq(n4(i),i=5..27);

Mathematica

Join[{0, 0}, LinearRecurrence[{13, -67, 175, -244, 172, -48}, {0, 0, 0, 32, 300, 1852}, 25]] (* Jean-François Alcover, Sep 02 2018 *)

PARI

a(n) = { if (n<2, 0, 2*n - 7 + (6 - n)*2^(n - 1) - 3^n + 4^(n - 1)) } \\ Harry J. Smith, Jul 02 2009

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).

Extensions

Edited by N. J. A. Sloane, Nov 11 2006