|
| |
|
|
A000486
|
|
One half of the number of permutations of [n] such that the differences have 4 runs with the same signs.
(Formerly M5011 N2158)
|
|
4
|
|
|
|
16, 150, 926, 4788, 22548, 100530, 433162, 1825296, 7577120, 31130190, 126969558, 515183724, 2082553132, 8395437930, 33776903714, 135691891272, 544517772984, 2183315948550, 8748985781230, 35043081823140, 140313684667076
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
