A294708 Number of permutations of [n] avoiding {4231, 2143, 1234}.

1, 1, 2, 6, 21, 69, 190, 446, 927, 1745, 3036, 4960, 7701, 11467, 16490, 23026, 31355, 41781, 54632, 70260, 89041, 111375, 137686, 168422, 204055, 245081, 292020, 345416, 405837, 473875, 550146, 635290, 729971, 834877, 950720, 1078236, 1218185, 1371351, 1538542, 1720590

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 4.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

From Colin Barker, Nov 10 2017: (Start)

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

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>10.

a(n) = (1/6)*(786 - 787*n + 333*n^2 - 68*n^3 + 6*n^4) for n>5.

(End)

Maple

cn := [1, -4, 7, -4, 6, 8, 4, 4, 6, -6, 2] ;
p := add(cn[i]*x^(i-1), i=1..nops(cn)) ;
q := (1-x)^5 ;
taylor(p/q, x=0, 40) ;
gfun[seriestolist](%) ;

Prog

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

Crossrefs

Sequence in context: A294706 A294707 A116842 * A294709 A116774 A116756

Adjacent sequences: A294705 A294706 A294707 * A294709 A294710 A294711

Keyword

nonn,easy

Author

R. J. Mathar, Nov 07 2017

Status

approved