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A116754 Number of permutations of length n which avoid the patterns 2134, 2143, 4312. 1
1, 2, 6, 21, 73, 239, 734, 2134, 5934, 15918, 41470, 105470, 262910, 644350, 1556478, 3713022, 8761342, 20475902, 47448062, 109117438, 249233406, 565772286, 1277165566, 2868379646, 6412042238, 14272167934, 31641829374, 69893881854, 153863847934, 337641471998 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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 83.
FORMULA
G.f.: x*(1 - 7*x + 20*x^2 - 25*x^3 + 12*x^4 - 2*x^5 - x^6) / ((1 - x)*(1 - 2*x)^4).
a(n) = (1/128)*(4*(-64 + 65*2^n) - 107*2^n*n + 9*2^(1+n)*n^2 + 2^n*n^3) for n > 2. - Colin Barker, Nov 02 2017
MATHEMATICA
CoefficientList[Series[(1 - 7*x + 20*x^2 - 25*x^3 + 12*x^4 - 2*x^5 - x^6)/((1 - x)*(1 - 2*x)^4), {x, 0, 40}], x] (* Wesley Ivan Hurt, Dec 26 2023 *)
PROG
(PARI) Vec(x*(1 - 7*x + 20*x^2 - 25*x^3 + 12*x^4 - 2*x^5 - x^6) / ((1 - x)*(1 - 2*x)^4) + O(x^30)) \\ Colin Barker, Nov 02 2017
CROSSREFS
Sequence in context: A116839 A294800 A116776 * A294801 A116768 A294694
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Feb 26 2006
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)