A294802 Number of permutations of [n] avoiding {3412, 3421, 1324}.

1, 1, 2, 6, 21, 73, 240, 744, 2192, 6192, 16896, 44800, 115968, 294144, 733184, 1800192, 4362240, 10448896, 24772608, 58195968, 135593984, 313589760, 720371712, 1644691456, 3733979136, 8433696768, 18958254080, 42429579264, 94573166592, 210000412672, 464661774336, 1024752353280, 2252978782208

Offset

0,3

Links

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

D. Callan and T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 [math.CO] (2017), Table 1 No 88.

Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).

Formula

G.f.: (1 - x)^2*(1 - 5*x + 7*x^2 + x^3) / (1 - 2*x)^4.

From Colin Barker, Nov 09 2017: (Start)

a(n) = 2^(n-6)*(36 - 8*n + n^2 + n^3) for n>1.

a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4) for n>5.

(End)

Maple

(1 -x)^2*(1 -5*x +7*x^2 +x^3)/(1 -2*x)^4 ;
taylor(%, x=0, 40) ;
gfun[seriestolist](%) ;

Prog

(PARI) Vec((1 - x)^2*(1 - 5*x + 7*x^2 + x^3) / (1 - 2*x)^4 + O(x^30)) \\ Colin Barker, Nov 09 2017

Crossrefs

Sequence in context: A116768 A294694 A116740 * A116788 A294695 A116778

Adjacent sequences: A294799 A294800 A294801 * A294803 A294804 A294805

Keyword

nonn,easy

Author

R. J. Mathar, Nov 09 2017

Status

approved