A294771 Number of permutations of [n] avoiding {4231, 2341, 4123}.

1, 1, 2, 6, 21, 75, 259, 862, 2808, 9090, 29489, 96076, 314011, 1027749, 3364559, 11012071, 36033146, 117891838, 385711145, 1261999184, 4129291969, 13511534900, 44211907218, 144668866862, 473380823897, 1548980397627, 5068520414694, 16585048409912, 54269098388346, 177577820365484

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 152.

Index entries for linear recurrences with constant coefficients, signature (10,-42,99,-144,134,-83,31,-5).

Formula

From Colin Barker, Apr 25 2020: (Start)

G.f.: (1 - x)^6*(1 - 3*x + x^2) / (1 - 10*x + 42*x^2 - 99*x^3 + 144*x^4 - 134*x^5 + 83*x^6 - 31*x^7 + 5*x^8).

a(n) = 10*a(n-1) - 42*a(n-2) + 99*a(n-3) - 144*a(n-4) + 134*a(n-5) - 83*a(n-6) + 31*a(n-7) - 5*a(n-8) for n>8.

(End)

Maple

(x-1)^6*(x^2-3*x+1)/(5*x^8-31*x^7+83*x^6-134*x^5+144*x^4-99*x^3+42*x^2-10*x+1) ;
taylor(%, x=0, 40) ;
gfun[seriestolist](%) ;

Prog

(PARI) Vec((1 - x)^6*(1 - 3*x + x^2) / (1 - 10*x + 42*x^2 - 99*x^3 + 144*x^4 - 134*x^5 + 83*x^6 - 31*x^7 + 5*x^8) + O(x^30)) \\ Colin Barker, Apr 25 2020

Crossrefs

Sequence in context: A116814 A294806 A294807 * A294814 A116816 A116742

Adjacent sequences: A294768 A294769 A294770 * A294772 A294773 A294774

Keyword

nonn,easy

Author

R. J. Mathar, Nov 08 2017

Status

approved