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Search: id:A136029
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| A136029 |
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a(n) is the number of central ideals of a garland of order 2n, i.e. a(n) = g(2n,n), where g(n,k) is the number of ideals of size k in a garland (or double fence) of order n (see A137278). |
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+0
1
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| 1, 1, 1, 3, 7, 15, 33, 75, 171, 391, 899, 2077, 4815, 11195, 26097, 60975, 142751, 334791, 786419, 1849905, 4357121, 10274313, 24252923, 57305241, 135521807, 320758587, 759757139, 1800838381, 4271267043, 10136815015, 24070870545
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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T. S. Blyth, J. C. Varlet, Ockham algebras, Oxford Science Pub. 1994.
E. Munarini, Enumeration of order ideals of a garland, Ars Combin. 76 (2005), 185--192.
Munarini, Emanuele, Combinatorial properties of the antichains of a garland. Integers, 9 (2009), 353-374.
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LINKS
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Emanuele Munarini (emanuele.munarini(AT)polimi.it), Mar 21 2008, Table of n, a(n) for n = 0..100
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FORMULA
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Recurrence: ( n + 6 ) a(n+6) - ( 2 n + 11 ) a(n+5) - ( n + 3 ) a(n+4) - 4 a(n+3) - ( n + 4 ) c_(n+2) - ( 2 n + 3 ) a(n+1) + ( n + 1 ) a(n) = 0 GF: a(x) = ( 1 - x^2 )/sqrt( 1 - 2 x - x^2 - x^4 + 2 x^5 + x^6 )
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EXAMPLE
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a(4) = 7, since the central ideals of the garland G(4):
5..6..7..8
o..o..o..o
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o..o..o..o
1..2..3..4
are: 1234, 1253, 1254, 1236, 2347, 1348, 2348.
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CROSSREFS
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Sequence in context: A146654 A026701 A140498 this_sequence A101892 A147102 A147379
Adjacent sequences: A136026 A136027 A136028 this_sequence A136030 A136031 A136032
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KEYWORD
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easy,nonn
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AUTHOR
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Emanuele Munarini (emanuele.munarini(AT)polimi.it), Mar 21 2008
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