A294048 Number of permutations of [n] avoiding {2143, 1432, 1324}.

1, 1, 2, 6, 21, 77, 289, 1103, 4261, 16603, 65100, 256466, 1014107, 4021836, 15988827, 63691619, 254145940, 1015570446, 4063266013, 16274491491, 65245082548, 261786577155, 1051150840105, 4223435727598, 16979312455238, 68297061505195, 274846004875298, 1106529463859781

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..1646

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 227.

Formula

D-finite with recurrence (-n+1)*a(n) +3*(4*n-7)*a(n-1) +(-56*n+143)*a(n-2) +6*(23*n-80)*a(n-3) +(-214*n+979)*a(n-4) +9*(24*n-139)*a(n-5) +4*(-35*n+248)*a(n-6) +(49*n-418)*a(n-7) +3*(-n+13)*a(n-8) +2*(-2*n+17)*a(n-9)=0. - R. J. Mathar, Mar 11 2021

Maple

C := (1-sqrt(1-4*x))/2/x ;
(1 -6*x +12*x^2 -12*x^3 +6*x^4 -x^5 -x^2*(1 -x +x^2)^2*C)/(1 -7*x +16*x^2 -19*x^3 +11*x^4 -2*x^5 -x^6) ;
taylor(%, x=0, 40) ;
gfun[seriestolist](%) ;

Crossrefs

Sequence in context: A242622 A279561 A360150 * A375443 A063023 A150188

Adjacent sequences: A294045 A294046 A294047 * A294049 A294050 A294051

Keyword

nonn,easy

Author

R. J. Mathar, Nov 09 2017

Status

approved