A294718 Number of permutations of [n] avoiding {4231, 2134, 1243}.

1, 1, 2, 6, 21, 70, 205, 536, 1264, 2722, 5424, 10122, 17871, 30102, 48703, 76108, 115394, 170386, 245770, 347214, 481497, 656646, 882081, 1168768, 1529380, 1978466, 2532628, 3210706, 4033971, 5026326, 6214515, 7628340, 9300886, 11268754, 13572302, 16255894, 19368157, 22962246

Offset

0,3

Links

Colin Barker, Table of n, a(n) for n = 0..1000

D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 [math.CO] (2017), Table 2 No 14.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

From Colin Barker, Nov 10 2017: (Start)

G.f.: (1 - 6*x + 16*x^2 - 22*x^3 + 21*x^4 - 7*x^5 + 2*x^6 + 10*x^7 - 11*x^8 + 4*x^9) / (1 - x)^7.

a(n) = (1/360)*(16560 - 13902*n + 4501*n^2 - 825*n^3 + 175*n^4 - 33*n^5 + 4*n^6) for n>2.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>9.

(End)

Maple

cn := [1, -6, 16, -22, 21, -7, 2, 10, -11, 4] ;
p := add(cn[i]*x^(i-1), i=1..nops(cn)) ;
q := (1-x)^7 ;
taylor(p/q, x=0, 40) ;
gfun[seriestolist](%) ;

Mathematica

LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 1, 2, 6, 21, 70, 205, 536, 1264, 2722}, 40] (* Harvey P. Dale, May 27 2018 *)

Prog

(PARI) Vec((1 - 6*x + 16*x^2 - 22*x^3 + 21*x^4 - 7*x^5 + 2*x^6 + 10*x^7 - 11*x^8 + 4*x^9) / (1 - x)^7 + O(x^40)) \\ Colin Barker, Nov 10 2017

Crossrefs

Sequence in context: A116804 A116832 A116811 * A116794 A294719 A116795

Adjacent sequences: A294715 A294716 A294717 * A294719 A294720 A294721

Keyword

nonn,easy

Author

R. J. Mathar, Nov 07 2017

Status

approved