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A116749
Number of permutations of length n which avoid the patterns 1423, 3124, 3421.
1
1, 2, 6, 21, 71, 219, 626, 1698, 4452, 11428, 28966, 72907, 182915, 458590, 1150877, 2894324, 7299391, 18468191, 46885660, 119437550, 305268086, 782671392, 2012470416, 5188157511, 13406252581, 34712884554, 90042441271, 233921270608
OFFSET
1,2
LINKS
D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 (2017), Table 2 No 31.
Index entries for linear recurrences with constant coefficients, signature (13,-73,232,-459,585,-479,242,-68,8).
FORMULA
G.f.: (5*x^9-30*x^8+80*x^7-153*x^6+230*x^5-231*x^4+143*x^3-53*x^2+11*x-1)*x/((x-1)^4*(2*x-1)^3*(x^2-3*x+1)).
a(n) = 2^(n-5)*(n+9)*(n-2) -(n-1)*(n^2+4*n-6)/6 +A001906(n), n>=1. - R. J. Mathar, Jan 11 2024
MATHEMATICA
Rest@ CoefficientList[Series[(5 x^9 - 30 x^8 + 80 x^7 - 153 x^6 + 230 x^5 - 231 x^4 + 143 x^3 - 53 x^2 + 11 x - 1) x/((x - 1)^4 (2 x - 1)^3 (x^2 - 3 x + 1)), {x, 0, 28}], x] (* Michael De Vlieger, Feb 18 2017 *)
PROG
(PARI) Vec((5*x^9-30*x^8+80*x^7-153*x^6+230*x^5-231*x^4+143*x^3-53*x^2+11*x-1)*x/((x-1)^4*(2*x-1)^3*(x^2-3*x+1)) + O(x^30)) \\ Michel Marcus, Feb 17 2017
CROSSREFS
Sequence in context: A294726 A294700 A294701 * A116792 A116761 A116807
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Feb 26 2006
STATUS
approved