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A046718
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Number of permutations of [ n ] with exactly one 132-pattern and two 123-patterns.
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5
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1, 4, 14, 47, 152, 472, 1408, 4048, 11264, 30464, 80384, 207616, 526336, 1312768, 3227648, 7835648, 18808832, 44695552, 105250816, 245825536, 569901056, 1312292864, 3003121664, 6833569792, 15468593152, 34846277632, 78148272128, 174533378048, 388291887104
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OFFSET
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4,2
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LINKS
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FORMULA
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G.f.: -x^4*(x^3-6*x^2+4*x-1)/(2*x-1)^4.
a(n) = 2^(n-8)*(n^3-11*n^2+54*n-88). - R. J. Mathar, Oct 02 2012
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EXAMPLE
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a(4) = 1: 1324.
a(5) = 4: 24315, 24351, 41325, 51324.
a(6) = 14: 354216, 354261, 354612, 354621, 435162, 462135, 524316, 524361, 541326, 561324, 624315, 624351, 641325, 651324.
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MAPLE
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a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <-16|32|-24|8>>^(n-4).
<<1, 4, 14, 47>>)[1, 1]:
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MATHEMATICA
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PROG
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(Sage)
def LinearRecurrence4(a0, a1, a2, a3, a4, a5, a6, a7):
x, y, z, u = Integer(a0), Integer(a1), Integer(a2), Integer(a3)
yield x
while True:
x, y, z, u = y, z, u, a7*x+a6*y+a5*z+a4*u
yield x
A046718 = LinearRecurrence4(1, 4, 14, 47, 8, -24, 32, -16)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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