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A116722
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Number of permutations of length n which avoid the patterns 312, 1324, 3421; or avoid the patterns 312, 1324, 2341, etc.
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2
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1, 2, 5, 12, 25, 47, 82, 135, 212, 320, 467, 662, 915, 1237, 1640, 2137, 2742, 3470, 4337, 5360, 6557, 7947, 9550, 11387, 13480, 15852, 18527, 21530, 24887, 28625, 32772, 37357, 42410, 47962, 54045, 60692, 67937, 75815, 84362, 93615, 103612, 114392, 125995
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: x*(1 - 3*x + 5*x^2 - 3*x^3 + x^5) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>4. - Colin Barker, Oct 24 2017
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PROG
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(PARI) Vec(x*(1 - 3*x + 5*x^2 - 3*x^3 + x^5) / (1 - x)^5 + O(x^60)) \\ Colin Barker, Oct 24 2017
(Magma) [1] cat [(n^4 - 6*n^3 + 47*n^2 - 114*n + 120)/24 : n in [2..50]]; // Wesley Ivan Hurt, Mar 25 2020
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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