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A114215 Number of derangements of [n] avoiding the patterns 123, 132 and 213. 1
0, 1, 2, 4, 4, 9, 12, 25, 30, 64, 80, 169, 208, 441, 546, 1156, 1428, 3025, 3740, 7921, 9790, 20736, 25632, 54289, 67104, 142129, 175682, 372100, 459940, 974169, 1204140, 2550409, 3152478, 6677056, 8253296, 17480761, 21607408, 45765225 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

T. Mansour and A. Robertson, Refined restricted permutations avoiding subsets of patterns of length three, Annals of Combinatorics, 6, 2002, 407-418; Theorem 3.2.

Index entries for linear recurrences with constant coefficients, signature (0,2,0,2,0,-1).

FORMULA

a(n) = F(n)-F((n-2)/2)^2 if n is even; a(n)=F(n)-F((n-1)/2)^2 if n is odd; here F(n) is the Fibonacci sequence with F(0)=F(1)=1.

a(n) = 2*a(n-2)+2*a(n-4)-a(n-6). G.f.: -x^2*(x+1)*(x^3-x^2-x-1) / ((x^2-x-1)*(x^2+1)*(x^2+x-1)). - Colin Barker, Mar 29 2014

EXAMPLE

a(2)=1 because we have 21; a(3)=2 because we have 231 and 312; a(4)=4 because we have 3412,3421,4312 and 4321.

MAPLE

with(combinat): F:=n->fibonacci(n+1): a:=proc(n) if n mod 2 = 0 then F(n)-F((n-2)/2)^2 else F(n)-F((n-1)/2)^2 fi end: seq(a(n), n=1..45);

MATHEMATICA

CoefficientList[Series[- x (x + 1) (x^3 - x^2 - x - 1)/((x^2 - x - 1) (x^2 + 1) (x^2 + x - 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 29 2014 *)

CROSSREFS

Cf. A007598 (bisection), A079472 (bisection).

Sequence in context: A335057 A039887 A216162 * A292302 A151712 A253827

Adjacent sequences:  A114212 A114213 A114214 * A114216 A114217 A114218

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Nov 17 2005

STATUS

approved

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Last modified May 31 19:40 EDT 2020. Contains 334748 sequences. (Running on oeis4.)