A294765 Number of permutations of [n] avoiding {4231, 1423, 1234}.

1, 1, 2, 6, 21, 74, 245, 744, 2068, 5296, 12608, 28150, 59412, 119341, 229477, 424478, 758491, 1313931, 2213350, 3635214, 5834559, 9169668, 14136101, 21409620, 31899782, 46816226, 67749956, 96772222, 136553926, 190508831, 262964229, 359363130, 486502469, 652812293, 868681386, 1146835318, 1502773465

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 115.

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Formula

G.f.: (1 - 10*x + 46*x^2 - 126*x^3 + 230*x^4 - 289*x^5 + 256*x^6 - 158*x^7 + 66*x^8 - 17*x^9 + 2*x^10) / (1 - x)^11.

From Colin Barker, Nov 11 2017: (Start)

a(n) = (3628800 - 1447200*n + 1660536*n^2 - 377700*n^3 + 154790*n^4 + 9135*n^5 - 987*n^6 + 1350*n^7 + 60*n^8 + 15*n^9 + n^10) / 3628800.

a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>10.

(End)

Maple

-(2*x^10-17*x^9+66*x^8-158*x^7+256*x^6-289*x^5+230*x^4-126*x^3+46*x^2-10*x+1)/(x-1)^11   ;
taylor(%, x=0, 40) ;
gfun[seriestolist](%) ;

Prog

(PARI) Vec((1 - 10*x + 46*x^2 - 126*x^3 + 230*x^4 - 289*x^5 + 256*x^6 - 158*x^7 + 66*x^8 - 17*x^9 + 2*x^10) / (1 - x)^11 + O(x^40)) \\ Colin Barker, Nov 11 2017

Crossrefs

Sequence in context: A148488 A148489 A116771 * A116745 A116831 A294698

Adjacent sequences: A294762 A294763 A294764 * A294766 A294767 A294768

Keyword

nonn,easy

Author

R. J. Mathar, Nov 08 2017

Status

approved