A294700 Number of permutations of [n] avoiding {1324, 2143, 3421}.

1, 1, 2, 6, 21, 71, 218, 610, 1585, 3895, 9186, 21022, 47061, 103663, 225618, 486626, 1042305, 2220303, 4708714, 9949294, 20956661, 44022231, 92253162, 192912386, 402622961, 838825351, 1744789138, 3623830750, 7516137525, 15569193055, 32212182306, 66571910722

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 1 No 29.

Index entries for linear recurrences with constant coefficients, signature (9,-34,70,-85,61,-24,4).

Formula

G.f.: (1 - 8*x + 27*x^2 - 48*x^3 + 50*x^4 - 30*x^5 + 6*x^6) / ((1 - x)^5*(1 - 2*x)^2).

From Colin Barker, Nov 10 2017: (Start)

a(n) = (1/12)*(12 + 4*(3*2^n-4)*n - 5*n^2 - 2*n^3 - n^4).

a(n) = 9*a(n-1) - 34*a(n-2) + 70*a(n-3) - 85*a(n-4) + 61*a(n-5) - 24*a(n-6) + 4*a(n-7) for n>6.

(End)

Maple

p := 1-8*x+27*x^2-48*x^3+50*x^4-30*x^5+6*x^6 ;
q := (1-x)^5*(1-2*x)^2 ;
taylor(p/q, x=0, 40) ;
gfun[seriestolist](%) ;

Mathematica

LinearRecurrence[{9, -34, 70, -85, 61, -24, 4}, {1, 1, 2, 6, 21, 71, 218}, 40] (* Harvey P. Dale, Mar 18 2024 *)

Prog

(PARI) Vec((1 - 8*x + 27*x^2 - 48*x^3 + 50*x^4 - 30*x^5 + 6*x^6) / ((1 - x)^5*(1 - 2*x)^2) + O(x^40)) \\ Colin Barker, Nov 10 2017

Crossrefs

Sequence in context: A116833 A116808 A294726 * A294701 A116749 A116792

Adjacent sequences: A294697 A294698 A294699 * A294701 A294702 A294703

Keyword

nonn,easy

Author

R. J. Mathar, Nov 07 2017

Status

approved