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A116722 Number of permutations of length n which avoid the patterns 312, 1324, 3421; or avoid the patterns 312, 1324, 2341, etc. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Ângela Mestre, José Agapito, Square Matrices Generated by Sequences of Riordan Arrays, J. Int. Seq., Vol. 22 (2019), Article 19.8.4.
FORMULA
G.f.: x*(1 - 3*x + 5*x^2 - 3*x^3 + x^5) / (1 - x)^5.
For n >= 2, a(n) = (n^4 - 6*n^3 + 47*n^2 - 114*n + 120)/24. - Franklin T. Adams-Watters, Sep 16 2006
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
PROG
(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
CROSSREFS
Sequence in context: A002836 A116720 A116731 * A368638 A116730 A240847
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Feb 26 2006
EXTENSIONS
Extended beyond a(30) by R. J. Mathar, Aug 05 2008
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)