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

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

Offset: 5

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Examples

			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.
		

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).

Crossrefs

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

Equals 1/2 * A060158(n).

Programs

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 *)

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

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

Extensions

Edited by Emeric Deutsch, Feb 18 2004