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A294725
Number of permutations of [n] avoiding {4231, 3412, 1234}.
1
1, 1, 2, 6, 21, 71, 212, 554, 1289, 2725, 5326, 9758, 16941, 28107, 44864, 69266, 103889, 151913, 217210, 304438, 419141, 567855, 758220, 999098, 1300697, 1674701, 2134406, 2694862, 3373021, 4187891, 5160696, 6315042, 7677089, 9275729, 11142770, 13313126, 15825013, 18720151, 22043972
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 2 No 24.
FORMULA
From Colin Barker, Nov 10 2017: (Start)
G.f.: (1 - 6*x + 16*x^2 - 22*x^3 + 21*x^4 - 6*x^5 + 2*x^6) / (1 - x)^7.
a(n) = (1/120)*(120 - 40*n + 44*n^2 - 15*n^3 + 15*n^4 - 5*n^5 + n^6).
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>6.
(End)
MAPLE
cn := [1, -6, 16, -22, 21, -6, 2] ;
p := add(cn[i]*x^(i-1), i=1..nops(cn)) ;
q := (1-x)^7 ;
taylor(p/q, x=0, 40) ;
gfun[seriestolist](%) ;
PROG
(PARI) Vec((1 - 6*x + 16*x^2 - 22*x^3 + 21*x^4 - 6*x^5 + 2*x^6) / (1 - x)^7 + O(x^40)) \\ Colin Barker, Nov 10 2017
CROSSREFS
Sequence in context: A116767 A116759 A116835 * A116755 A116833 A116808
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Nov 07 2017
STATUS
approved