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Search: id:A052980
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| A052980 |
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G.f.: (1-x)/(1-2*x-x^3). |
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+0
5
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| 1, 1, 2, 5, 11, 24, 53, 117, 258, 569, 1255, 2768, 6105, 13465, 29698, 65501, 144467, 318632, 702765, 1549997, 3418626, 7540017, 16630031, 36678688, 80897393, 178424817, 393528322, 867954037, 1914332891, 4222194104, 9312342245
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n) counts permutations of length n which embed into the (infinite) increasing oscillating sequence given by 4,1,6,3,8,5,...,2k+2,2k-1,...; these are also the permutations which avoid {321, 2341, 3412, 4123}. - Vince Vatter (vince(AT)mcs.st-and.ac.uk), May 23 2008
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REFERENCES
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R. Brignall, N. Ruskuc and V. Vatter, Simple permutations: decidability and unavoidable substructures, Theoretical Computer Science 391 (2008), 150-163.
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1053
V. Vatter, Small permutation classes.
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FORMULA
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Recurrence: {a(1)=1, a(0)=1, a(2)=2, a(n)+2*a(n+2)-a(n+3)}
Sum(1/59*(4+3*_alpha^2+17*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+2*_Z+_Z^3))
G.f.: (1-x)/(1-2*x-x^3) - Vince Vatter (vince(AT)mcs.st-and.ac.uk), May 23 2008
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MAPLE
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spec := [S, {S=Sequence(Prod(Union(Prod(Z, Z, Z), Z), Sequence(Z)))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
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CROSSREFS
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See A110513 for another version.
Sequence in context: A134389 A111297 A077864 this_sequence A110513 A018115 A018007
Adjacent sequences: A052977 A052978 A052979 this_sequence A052981 A052982 A052983
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 05 2000
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