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A116734
Number of permutations of length n which avoid the patterns 231, 1432, 4123.
1
1, 2, 5, 12, 25, 50, 97, 184, 345, 642, 1189, 2196, 4049, 7458, 13729, 25264, 46481, 85506, 157285, 289308, 532137, 978770, 1800257, 3311208, 6090281, 11201794, 20603333, 37895460, 69700641, 128199490, 235795649, 433695840, 797691041
OFFSET
1,2
FORMULA
G.f.: A(x) = -{x(x^2+x^3+1-x)}/{(x-1)^2(x^3+x^2+x-1)}
a(n)=A000213(n+2)-n-1. [From R. J. Mathar, Aug 05 2008]
a(0)=0, a(1)=1, a(2)=2, then a(n) = a(n-1) + a(n-2) + a(n-3) + 2*n - 4. [From Gerald McGarvey, Oct 06 2009]
MATHEMATICA
LinearRecurrence[{3, -2, 0, -1, 1}, {1, 2, 5, 12, 25}, 40] (* Harvey P. Dale, Jan 21 2016 *)
CROSSREFS
Sequence in context: A240847 A166106 A067331 * A101836 A262667 A122439
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Feb 26 2006
EXTENSIONS
Extended beyond a(30) by R. J. Mathar, Aug 05 2008
STATUS
approved