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A104854
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Number of n-digit numbers using digits 0 to n-1 each exactly once and containing no 3-digit sequence in increasing or decreasing order.
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2
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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
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listen;
history;
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OFFSET
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1,3
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COMMENTS
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Leading zeros are not allowed, but digits > 9 are permitted.
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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LINKS
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FORMULA
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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;
G.f.: 1 + x + 3*x^2 + 8*x^3 + 27*x^4 + 106*x^5 + 483*x^6 + 2498*x^7 + ...
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MAPLE
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A001250 := proc(n) local x; if n = 1 then 1; else n!*coeftayl( 2*(tan(x)+sec(x)), x=0, n) ; fi ; end: A104854 := proc(n) if n <= 2 then 1; else A001250(n)-A001250(n-1)/2 ; fi ; end: seq(A104854(n), n=1..30) ; # R. J. Mathar, Feb 14 2008
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MATHEMATICA
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m = 23;
CoefficientList[1 + (Sec[x] + Tan[x] - 1)(Sec[x] + Tan[x]) + O[x]^m, x]* Range[0, m - 1]! (* Jean-François Alcover, Mar 31 2020 *)
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PROG
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(Python)
from itertools import accumulate, islice
def A104854_gen(): # generator of terms
yield 1
blist = (0, 1)
while True:
yield -blist[-1]+2*(blist := tuple(accumulate(reversed(blist), initial=0)))[-1]
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CROSSREFS
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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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STATUS
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approved
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