A294799 Number of permutations of [n] avoiding {3412, 1324, 2341}.

1, 1, 2, 6, 21, 73, 238, 721, 2046, 5501, 14158, 35172, 84895, 200133, 462714, 1052727, 2363200, 5245849, 11535354, 25163458, 54518249, 117424881, 251631318, 536828413, 1140787234, 2415828037, 5100146838, 10737245792, 22548348403, 47244338829, 98783858242, 206157933027

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 76.

Index entries for linear recurrences with constant coefficients, signature (11,-53,147,-259,301,-231,113,-32,4).

Formula

G.f.: (1 - 10*x + 44*x^2 - 110*x^3 + 173*x^4 - 176*x^5 + 114*x^6 - 45*x^7 + 12*x^8 - 4*x^9) / ((1 - x)^7*(1 - 2*x)^2).

From Colin Barker, Nov 09 2017: (Start)

a(n) = (1/720)*(-20160*(2^n-1) + 36*(349 + 5*2^(4+n))*n + 1556*n^2 + 1095*n^3 - 115*n^4 + 21*n^5 - n^6) for n>0.

a(n) = 11*a(n-1) - 53*a(n-2) + 147*a(n-3) - 259*a(n-4) + 301*a(n-5) - 231*a(n-6) + 113*a(n-7) - 32*a(n-8) + 4*a(n-9) for n > 9.

(End)

Maple

(1 -10*x +44*x^2 -110*x^3 +173*x^4 -176*x^5 +114*x^6 -45*x^7 +12*x^8 -4*x^9) /((1-x)^7 *(1-2*x)^2) ;
taylor(%, x=0, 40) ;
gfun[seriestolist](%) ;

Prog

(PARI) Vec( (1 - 10*x + 44*x^2 - 110*x^3 + 173*x^4 - 176*x^5 + 114*x^6 - 45*x^7 + 12*x^8 - 4*x^9) / ((1 - x)^7*(1 - 2*x)^2) + O(x^30)) \\ Colin Barker, Nov 09 2017

Crossrefs

Sequence in context: A294797 A294763 A294798 * A294693 A116757 A116839

Adjacent sequences: A294796 A294797 A294798 * A294800 A294801 A294802

Keyword

nonn,easy

Author

R. J. Mathar, Nov 09 2017

Status

approved