The On-Line Encyclopedia of Integer Sequences (OEIS)

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A082971

Number of permutations of {1,2,...,n} containing exactly 3 occurrences of the 132 pattern.
(history; published version)

#30 by Charles R Greathouse IV at Thu Sep 08 08:45:10 EDT 2022

PROG

(MAGMAMagma) [1] cat [(n^6+51*n^5-407*n^4-99*n^3+7750*n^2-22416*n+20160)* Factorial(2*n-9)/(6*Factorial(n)*Factorial(n-5)): n in [5..30]]; // Vincenzo Librandi, Oct 30 2018

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#29 by Bruno Berselli at Tue Oct 30 04:35:44 EDT 2018

STATUS

editing

approved

#28 by Bruno Berselli at Tue Oct 30 04:35:36 EDT 2018

PROG

(MAGMA) [1] cat [(n^6+51*n^5-407*n^4-99*n^3+7750*n^2-22416*n+20160)* Factorial(2*n-9)/(6*Factorial(n)*Factorial(n-5)): n in [5..30]]; // Vincenzo Librandi, Oct 30 2018

#27 by Bruno Berselli at Tue Oct 30 04:33:35 EDT 2018

MATHEMATICA

a[4] = 1; a[n_] := (n^6 + 51n51 n^5 - 407n407 n^4 - 99n99 n^3 + 7750n7750 n^2 - 22416n 22416 n + 20160) (2n 2 n - 9)!/(6 n! (n - 5)!);

PROG

(MAGMA) [1] cat [(n^6+51*n^5-407*n^4-99*n^3+7750*n^2-22416*n+20160)*Factorial(2*n - 9) / (6*Factorial(n) / 6 / *Factorial(n - 5)*(n^6 + 51*n^5 - 407*n^4 - 99*n^3 + 7750*n^2 - 22416*n + 20160): n in [5..30]]; // Vincenzo Librandi, Oct 30 2018

#26 by Bruno Berselli at Tue Oct 30 04:30:52 EDT 2018

STATUS

proposed

editing

#25 by Vincenzo Librandi at Tue Oct 30 03:30:59 EDT 2018

STATUS

editing

proposed

#24 by Vincenzo Librandi at Tue Oct 30 03:30:43 EDT 2018

DATA

1, 14, 82, 410, 1918, 8657, 38225, 166322, 716170, 3059864, 12994936, 54924212, 231235054, 970347575, 4060697955, 16952812170, 70629116910, 293720506860, 1219498444500, 5055891511980, 20933654593020, 86571545598642, 357628915621698, 1475896409177780

LINKS

Vincenzo Librandi, <a href="/A082971/b082971.txt">Table of n, a(n) for n = 4..1000</a>

PROG

(MAGMA) [1] cat [Factorial(2*n - 9) / Factorial(n) / 6 / Factorial(n - 5)*(n^6 + 51*n^5 - 407*n^4 - 99*n^3 + 7750*n^2 - 22416*n + 20160): n in [5..30]]; // Vincenzo Librandi, Oct 30 2018

STATUS

proposed

editing

#23 by Michel Marcus at Tue Oct 30 03:07:18 EDT 2018

STATUS

editing

proposed

#22 by Michel Marcus at Tue Oct 30 03:07:16 EDT 2018

LINKS

T. Mansour and A. Vainshtein, <a href="httphttps://arXivarxiv.org/abs/math.CO/0105073">Counting occurrences of 132 in a permutation</a>, arXiv:math/0105073 [math.CO], 2001.

STATUS

proposed

editing

#21 by Jean-François Alcover at Tue Oct 30 03:05:50 EDT 2018

STATUS

editing

proposed