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A116706
Number of permutations of length n which avoid the patterns 2134, 3421.
1
1, 2, 6, 22, 86, 330, 1206, 4174, 13726, 43134, 130302, 380414, 1078270, 2978814, 8046590, 21311486, 55468030, 142147582, 359268350, 896794622, 2213543934, 5408292862, 13091995646, 31424774142, 74845257726, 176991240190, 415789744126, 970830381054
OFFSET
1,2
LINKS
Darla Kremer and Wai Chee Shiu, Finite transition matrices for permutations avoiding pairs of length four patterns, Discrete Math. 268 (2003), 171-183. MR1983276 (2004b:05006). See Table 1.
FORMULA
G.f.: x*(1 - 9*x + 34*x^2 - 64*x^3 + 64*x^4 - 28*x^5 + 4*x^6) / ((1 - x)*(1 - 2*x)^5)
From Colin Barker, Oct 20 2017: (Start)
a(n) = (24*(-32+39*2^n) - 263*2^(1+n)*n + 165*2^n*n^2 - 13*2^(1+n)*n^3 + 3*2^n*n^4) / 384 for n>1.
a(n) = 11*a(n-1) - 50*a(n-2) + 120*a(n-3) - 160*a(n-4) + 112*a(n-5) - 32*a(n-6) for n>7.
(End)
PROG
(PARI) Vec(x*(1 - 9*x + 34*x^2 - 64*x^3 + 64*x^4 - 28*x^5 + 4*x^6) / ((1 - x)*(1 - 2*x)^5) + O(x^30)) \\ Colin Barker, Oct 20 2017
CROSSREFS
Sequence in context: A079104 A116705 A116708 * A165524 A165525 A165526
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Feb 26 2006
STATUS
approved