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A116726
Number of permutations of length n which avoid the patterns 213, 1234, 2431.
0
1, 2, 5, 12, 26, 55, 113, 227, 449, 877, 1696, 3254, 6203, 11762, 22205, 41766, 78316, 146467, 273313, 509041, 946531, 1757541, 3259480, 6038576, 11176989, 20671462, 38204837, 70567516, 130275854, 240394475
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. - From N. J. A. Sloane, Feb 01 2013
FORMULA
G.f.: A(x) = -(x^3-x+1)*x/((x-1)*(x^2+x-1)*(x^3+x^2+x-1)).
2*a(n) = 1 -2*A000045(n+4) +A303005(n+2). - R. J. Mathar, Jan 11 2024
MATHEMATICA
CoefficientList[Series[-(x(x^3-x+1))/((x-1)(x^2+x-1)(x^3+x^2+x-1)), {x, 0, 50}], x] (* Stefano Spezia, Nov 29 2018 *)
CROSSREFS
Sequence in context: A360785 A198896 A026688 * A228078 A125180 A073778
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Feb 26 2006
STATUS
approved