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Search: id:A135410
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| A135410 |
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a(n) = the number of permutations of (1,2,3,...n) each with the same up-down signature as its inverse permutation. |
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+0
1
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| 1, 2, 4, 10, 26, 80, 272, 1076, 4848, 24832, 142340, 902440
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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An "up-down signature" of the permutation (p(1),p(2),p(3),...p(n)) is the sequence of (n-1) signs (+ or -) where the kth sign in the sequence is the sign of (p(k+1)-p(k)). All permutations of (1,2,3,...n) which are their own inverses obviously have the same up-down signature as their inverse permutations.
The terms were calculated by R. J. Mathar (see link).
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
R. J. Mathar, C== program
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EXAMPLE
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The up-down signature of the permutation (4,2,6,3,5,1) is -+-+-. This permutation's inverse permutation is (6,2,4,1,5,3). The inverse permutation also has the up-down signature -+-+-. So these two permutations, among others, are included in the count for n = 6.
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CROSSREFS
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Sequence in context: A096807 A003239 A116673 this_sequence A148103 A148104 A086991
Adjacent sequences: A135407 A135408 A135409 this_sequence A135411 A135412 A135413
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KEYWORD
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more,nonn
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AUTHOR
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Leroy Quet Dec 10 2007
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