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Search: id:A104854
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| A104854 |
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Number of n-digit numbers using digits 0 to n-1 each exactly once and containig no 3-digit sequence in increasing or decreasing order. |
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+0
1
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| 1, 1, 3, 8, 27, 106, 483, 2498, 14487, 93106, 657063, 5051738, 42033747, 376353706, 3608153643, 36879266978, 400339173807, 4599894007906, 55772890550223, 711653491362218, 9532624918010667, 133746250733151706, 1961498898620566803
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Derived from A001250: 1, 2, 4, 10, 32, 122, 544, 2770, 15872, 101042, 707584, 5405530, ... giving 1, 1 and 4-2/2, 10-4/2, 32-10/2, 122-32/2=106, 544-122/2=483, ...
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EXAMPLE
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The n-digit numbers contributing to the counts are:
n=1: 0;
n=2: 10;
n=3: 102, 120, 201;
n=4: 1032, 1203, 1302, 2031, 2130, 2301, 3021, 3120;
n=5: 10324, 10423, 12043,...,41302, 42301;
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MAPLE
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A001250 := proc(n) local x; if n = 0 then 1; else (n+1)!*coeftayl( 2*(tan(x)+1/cos(x)), x=0, n+1) ; fi ; end: A104854 := proc(n) if n <= 2 then 1; else A001250(n-1)-A001250(n-2)/2 ; fi ; end: seq(A104854(n), n=1..30) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 14 2008
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CROSSREFS
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Sequence in context: A102318 A102206 A110886 this_sequence A030495 A074271 A005641
Adjacent sequences: A104851 A104852 A104853 this_sequence A104855 A104856 A104857
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KEYWORD
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nonn
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AUTHOR
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Michel Criton (mcriton(AT)wanadoo.fr), Apr 23 2005 and May 29 2005
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 14 2008
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