A000486 One half of the number of permutations of [n] such that the differences have 4 runs with the same signs. (Formerly M5011 N2158)

16, 150, 926, 4788, 22548, 100530, 433162, 1825296, 7577120, 31130190, 126969558, 515183724, 2082553132, 8395437930, 33776903714, 135691891272, 544517772984, 2183315948550, 8748985781230, 35043081823140, 140313684667076

Offset

5,1

References

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 260, #13

F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 260.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Vincenzo Librandi, Table of n, a(n) for n = 5..1000

Index entries for linear recurrences with constant coefficients, signature (13,-67,175,-244,172,-48).

Formula

Limit_{n->infinity} 8*a(n)/4^n = 1. - Philippe Deléham, Feb 22 2004

G.f.: 2*x^5*(24*x^2-29*x+8) / ((x-1)^2*(2*x-1)^2*(3*x-1)*(4*x-1)). - Colin Barker, Dec 21 2012

Example

a(5)=16 because the permutations of [5] with four sign runs are 13254, 14253, 14352, 15342, 15243, 21435, 21534, 23154, 24153, 25143, 31425, 31524, 32415, 32514, 41325, 42315 and their reversals.

Mathematica

CoefficientList[Series[2 (24 x^2 - 29 x + 8)/((x - 1)^2 (2 x - 1)^2 (3 x - 1) (4 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 13 2013 *)

Prog

(PARI) a(n)=([0, 1, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0; 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 1; -48, 172, -244, 175, -67, 13]^(n-5)*[16; 150; 926; 4788; 22548; 100530])[1, 1] \\ Charles R Greathouse IV, Jun 23 2020

Crossrefs

a(n) = T(n, 4), where T(n, k) is the array defined in A008970.

Equals 1/2 * A060158(n).

Sequence in context: A269137 A155657 A135458 * A223069 A006420 A221422

Adjacent sequences: A000483 A000484 A000485 * A000487 A000488 A000489

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Edited by Emeric Deutsch, Feb 18 2004

Status

approved