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A116716
Number of permutations of length n which avoid the patterns 321, 2341, 4123.
2
1, 2, 5, 12, 26, 58, 131, 295, 662, 1487, 3342, 7510, 16874, 37915, 85195, 191432, 430143, 966522, 2171756, 4879892, 10965017, 24638169, 55361464, 124396081, 279515456, 628065528, 1411250432, 3171050937, 7125286777, 16010374058, 35974983957, 80835055196
OFFSET
1,2
LINKS
David Lonoff and Jonah Ostroff, Symmetric Permutations Avoiding Two Patterns, Annals of Combinatorics 14 (1) pp.143-158 Springer, 2010; . - N. J. A. Sloane, Dec 27 2012
FORMULA
G.f.: x*(1 + x)*(1 - x + 2*x^2 - x^3) / ((1 + x^2)*(1 - 2*x - x^2 + x^3)).
a(n) = 2*a(n-1) + a(n-3) + a(n-4) - a(n-5) for n>5. - Colin Barker, Oct 20 2017
PROG
(PARI) Vec(x*(1 + x)*(1 - x + 2*x^2 - x^3) / ((1 + x^2)*(1 - 2*x - x^2 + x^3)) + O(x^40)) \\ Colin Barker, Oct 20 2017
CROSSREFS
Sequence in context: A073778 A033490 A221950 * A128812 A241692 A078410
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Feb 26 2006
STATUS
approved