A294797 Number of permutations of [n] avoiding {1243, 1324, 3412}.

1, 1, 2, 6, 21, 73, 237, 711, 1988, 5253, 13301, 32673, 78669, 187230, 443398, 1050209, 2497187, 5976456, 14419577, 35101838, 86229874, 213707024, 534022585, 1344450284, 3407215499, 8684458421, 22243751970, 57208235104, 147636483121, 382077767531, 991081141309, 2575597009441

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 1 No 72.

Index entries for linear recurrences with constant coefficients, signature (13,-74,243,-510,715,-678,429,-173,40,-4).

Formula

From Colin Barker, Nov 23 2017: (Start)

G.f.: (1 - 12*x + 63*x^2 - 189*x^3 + 358*x^4 - 447*x^5 + 367*x^6 - 192*x^7 + 64*x^8 - 10*x^9) / ((1 - x)^6*(1 - 2*x)^2*(1 - 3*x + x^2)).

a(n) = (1/120)*(3*2^(2-n)*(5*2^(2+n)*(-1+2^n) - (-5+sqrt(5))*(3+sqrt(5))^n + (3-sqrt(5))^n*(5+sqrt(5))) + 4*(-73+15*2^(1+n))*n - 120*n^2 - 65*n^3 - 3*n^5).

a(n) = 13*a(n-1) - 74*a(n-2) + 243*a(n-3) - 510*a(n-4) + 715*a(n-5) - 678*a(n-6) + 429*a(n-7) - 173*a(n-8) + 40*a(n-9) - 4*a(n-10) for n>9.

(End)

Maple

1+x*(1 -11*x +54*x^2 -152*x^3 +268*x^4 -311*x^5 +237*x^6 -109*x^7 +30*x^8 -4*x^9) /((1-x)^6 *(1-2*x)^2 *(1-3*x+x^2)) ;
taylor(%, x=0, 40) ;
gfun[seriestolist](%) ;

Prog

(PARI) Vec((1 - 12*x + 63*x^2 - 189*x^3 + 358*x^4 - 447*x^5 + 367*x^6 - 192*x^7 + 64*x^8 - 10*x^9) / ((1 - x)^6*(1 - 2*x)^2*(1 - 3*x + x^2)) + O(x^40)) \\ Colin Barker, Nov 23 2017

Crossrefs

Sequence in context: A294796 A116753 A294762 * A294763 A294798 A294799

Adjacent sequences: A294794 A294795 A294796 * A294798 A294799 A294800

Keyword

nonn,easy

Author

R. J. Mathar, Nov 09 2017

Status

approved