A294709 Number of permutations of [n] avoiding {2143, 3412, 1234}.

1, 1, 2, 6, 21, 69, 194, 470, 1009, 1969, 3562, 6062, 9813, 15237, 22842, 33230, 47105, 65281, 88690, 118390, 155573, 201573, 257874, 326118, 408113, 505841, 621466, 757342, 916021, 1100261, 1313034, 1557534, 1837185, 2155649, 2516834, 2924902, 3384277, 3899653, 4476002, 5118582

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 5.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

From Colin Barker, Nov 10 2017: (Start)

G.f.: (1 - 5*x + 11*x^2 - 11*x^3 + 10*x^4 + 2*x^5) / (1 - x)^6.

a(n) = (1/60)*(60 + 16*n - 65*n^2 + 70*n^3 - 25*n^4 + 4*n^5).

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>5.

(End)

Maple

cn := [1, -5, 11, -11, 10, 2] ;
p := add(cn[i]*x^(i-1), i=1..nops(cn)) ;
q := (1-x)^6 ;
taylor(p/q, x=0, 40) ;
gfun[seriestolist](%) ;

Mathematica

LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 1, 2, 6, 21, 69}, 40] (* Harvey P. Dale, Feb 26 2023 *)

Prog

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

Crossrefs

Sequence in context: A294707 A116842 A294708 * A116774 A116756 A116813

Adjacent sequences: A294706 A294707 A294708 * A294710 A294711 A294712

Keyword

nonn,easy

Author

R. J. Mathar, Nov 07 2017

Status

approved