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A116717
Number of permutations of length n which avoid the patterns 231, 1423, 3214.
1
1, 2, 5, 12, 26, 52, 98, 177, 310, 531, 895, 1491, 2463, 4044, 6611, 10774, 17520, 28446, 46136, 74771, 121116, 196117, 317485, 513877, 831661, 1345862, 2177873, 3524112, 5702390, 9226936, 14929790, 24157221, 39087538, 63245319, 102333451, 165579399, 267913515
OFFSET
1,2
LINKS
Michael Dairyko, Lara Pudwell, Samantha Tyner, Casey Wynn, Non-contiguous pattern avoidance in binary trees. Electron. J. Combin. 19 (2012), no. 3, Paper 22, 21 pp. MR2967227.
FORMULA
G.f.: -x*(x^4-x^3-2*x^2+2*x-1) / ((x^2+x-1)*(x-1)^3).
a(n) = A000045(n+5) - A000124(n+2). - Charlie Marion and Lara Pudwell, Jan 15 2014
From Colin Barker, Oct 20 2017: (Start)
a(n) = -3 + (2^(-1- n)*((1-sqrt(5))^n*(-11+5*sqrt(5)) + (1+sqrt(5))^n*(11+5*sqrt(5)))) / sqrt(5) - n - (1 + n)*(2 + n)/2.
a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 2*a(n-4) - a(n-5) for n>5.
(End)
a(n) = 1 + Sum_{k=1..n} Sum_{j=1..k} Sum_{i=1..j-1} Fibonacci(i). - Ehren Metcalfe, Oct 22 2017
MATHEMATICA
LinearRecurrence[{4, -5, 1, 2, -1}, {1, 2, 5, 12, 26}, 40] (* Vincenzo Librandi, Oct 22 2017 *)
PROG
(PARI) Vec(x*(1 - 2*x + 2*x^2 + x^3 - x^4) / ((1 - x)^3*(1 - x - x^2)) + O(x^40)) \\ Colin Barker, Oct 20 2017
(Magma) I:=[1, 2, 5, 12, 26]; [n le 5 select I[n] else 4*Self(n-1)-5*Self(n-2)+Self(n-3)+2*Self(n-4)-Self(n-5): n in [1..40]]; // Vincenzo Librandi, Oct 22 2017
CROSSREFS
Sequence in context: A132977 A027927 A221948 * A116725 A193263 A221949
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Feb 26 2006
STATUS
approved