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Search: id:A046740
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| A046740 |
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Triangle of number of permutations of [n] with 0 successions, by number of rises. |
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+0
4
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| 1, 1, 1, 2, 1, 8, 2, 1, 22, 28, 2, 1, 52, 182, 72, 2, 1, 114, 864, 974, 164, 2, 1, 240, 3474, 8444, 4174, 352, 2, 1, 494, 12660, 57194, 61464, 15782, 732, 2, 1, 1004, 43358, 332528, 660842, 373940, 55286, 1496, 2, 1, 2026, 142552, 1747558, 5814124
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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The recurrence given by Roselle is wrong.
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REFERENCES
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D. P. Roselle, Permutations by number of rises and successions, Proc. Amer. Math. Soc., 19 (1968), 8-16.
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FORMULA
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a(n, 1) = 1; for r > 1, a(n, r)=r*a(n-1, r)+(n-r)*a(n-1, r-1)+(n-2)*a(n-2, r-1).
a(n, 2) = 2^n-2*n = 2*A000295 = A005803, n >= 3.
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EXAMPLE
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1; 1; 1 2; 1 8 2; 1 22 28 2; ...
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CROSSREFS
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Cf. A046739, A000295. Row sums give A000255. Diagonals give A005803, A065340.
Row sums give A000255.
Sequence in context: A020778 A118961 A114706 this_sequence A130562 A011208 A001281
Adjacent sequences: A046737 A046738 A046739 this_sequence A046741 A046742 A046743
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KEYWORD
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nonn,easy,nice,tabf
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AUTHOR
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njas
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Jan 03 2003
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