A294770 Number of permutations of [n] avoiding {4231, 4123, 1234}.

1, 1, 2, 6, 21, 75, 253, 774, 2130, 5314, 12169, 25895, 51756, 98034, 177282, 307933, 516327, 839223, 1326868, 2046700, 3087767, 4565949, 6630075, 9469032, 13319968, 18477696, 25305411, 34246837, 45839926, 60732236, 79698120, 103657863, 133698909, 171099325, 217353654, 274201314, 343657705

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 144.

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

G.f.: (1 - 8*x + 29*x^2 - 60*x^3 + 81*x^4 - 66*x^5 + 40*x^6 - 15*x^7 + 3*x^8) / (1 - x)^9.

From Colin Barker, Nov 11 2017: (Start)

a(n) = (40320 - 22704*n + 33868*n^2 - 16996*n^3 + 6405*n^4 - 616*n^5 + 42*n^6 - 4*n^7 + 5*n^8) / 40320.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>8.

(End)

Maple

-(3*x^8-15*x^7+40*x^6-66*x^5+81*x^4-60*x^3+29*x^2-8*x+1)/(x-1)^9 ;
taylor(%, x=0, 40) ;
gfun[seriestolist](%) ;

Mathematica

LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 1, 2, 6, 21, 75, 253, 774, 2130}, 40] (* Harvey P. Dale, Dec 24 2023 *)

Prog

(PARI) Vec((1 - 8*x + 29*x^2 - 60*x^3 + 81*x^4 - 66*x^5 + 40*x^6 - 15*x^7 + 3*x^8) / (1 - x)^9 + O(x^40)) \\ Colin Barker, Nov 11 2017

Crossrefs

Sequence in context: A150186 A150187 A116818 * A116763 A116840 A116841

Adjacent sequences: A294767 A294768 A294769 * A294771 A294772 A294773

Keyword

nonn,easy

Author

R. J. Mathar, Nov 08 2017

Status

approved