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Search: id:A094718
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| A094718 |
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Array T read by antidiagonals: T(n,k) = number of involutions avoiding 132 and 12...k. |
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+0
12
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| 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 2, 1, 0, 1, 2, 3, 4, 1, 0, 1, 2, 3, 5, 4, 1, 0, 1, 2, 3, 6, 8, 8, 1, 0, 1, 2, 3, 6, 9, 13, 8, 1, 0, 1, 2, 3, 6, 10, 18, 21, 16, 1, 0, 1, 2, 3, 6, 10, 19, 27, 34, 16, 1, 0, 1, 2, 3, 6, 10, 20, 33, 54, 55, 32, 1, 0, 1, 2, 3, 6, 10, 20, 34, 61, 81, 89, 32, 1
(list; table; graph; listen)
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OFFSET
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1,8
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COMMENT
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Also, number of paths along a corridor with width k, starting from one side (from H. Bottomley's comment in A061551).
Rows converge to C(n,[n/2]) (A001405).
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LINKS
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T. Mansour, Restricted even permutations and Chebyshev polynomials
O. Guibert and T. Mansour, Restricted 132-involutions
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FORMULA
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G.f. for k-th row: 1/(xU(k, 1/2x)) * Sum[j=0..k-1, U(j, 1/2x)], with U(k, x) the Chebyshev polynomials of second kind.
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EXAMPLE
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0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1
1 2 2 4 4 8 8 16 16 32
1 2 3 5 8 13 21 34 55 89
1 2 3 6 9 18 27 54 81 162
1 2 3 6 10 19 33 61 108 197
1 2 3 6 10 20 34 68 116 232
1 2 3 6 10 20 35 69 124 241
1 2 3 6 10 20 35 70 125 250
1 2 3 6 10 20 35 70 126 251
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CROSSREFS
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Rows 3-8 are A016116, A000045, A038754, A028495, A030436, A061551.
Main diagonal is A014495, antidiagonal sums are in A094719.
Cf. A080934 (permutations).
Adjacent sequences: A094715 A094716 A094717 this_sequence A094719 A094720 A094721
Sequence in context: A080941 A114021 A053616 this_sequence A076191 A025861 A090723
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KEYWORD
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nonn,tabl
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AUTHOR
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Ralf Stephan, May 23 2004
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