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A294800
Number of permutations of [n] avoiding {1324, 2341, 3421}.
1
1, 1, 2, 6, 21, 73, 238, 726, 2101, 5857, 15926, 42626, 112997, 297861, 782666, 2052958, 5379953, 14091781, 36901646, 96621062, 252971401, 662305301, 1733959342, 4539590666, 11884834161, 31114937393, 81460008218, 213265122686, 558335401141, 1461741128617, 3826888039926, 10018923054526, 26229881196037
OFFSET
0,3
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 1 No 80.
FORMULA
G.f.: (1 - 7*x + 20*x^2 - 29*x^3 + 25*x^4 - 10*x^5 + 2*x^6) / ((1 - x)^5*(1 - 3*x + x^2)).
From Colin Barker, Nov 09 2017: (Start)
a(n) = (1/60)*(-3*2^(2-n)*(15*2^n + 2*(-5+sqrt(5))*(3+sqrt(5))^n - 2*(3-sqrt(5))^n*(5+sqrt(5))) + 80*n - 85*n^2 + 10*n^3 - 5*n^4).
a(n) = 8*a(n-1) - 26*a(n-2) + 45*a(n-3) - 45*a(n-4) + 26*a(n-5) - 8*a(n-6) + a(n-7) for n>6.
(End)
MAPLE
(1 -7*x +20*x^2 -29*x^3 +25*x^4 -10*x^5 +2*x^6)/((1 -x)^5*(1 -3*x +x^2)) ;
taylor(%, x=0, 40) ;
gfun[seriestolist](%) ;
PROG
(PARI) Vec((1 - 7*x + 20*x^2 - 29*x^3 + 25*x^4 - 10*x^5 + 2*x^6) / ((1 - x)^5*(1 - 3*x + x^2)) + O(x^30)) \\ Colin Barker, Nov 09 2017
CROSSREFS
Sequence in context: A294693 A116757 A116839 * A116776 A116754 A294801
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Nov 09 2017
STATUS
approved