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A104854 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. 2
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; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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, ...

LINKS

Table of n, a(n) for n=1..23.

D. Berry, J. Broom, D. Dixon, A. Flaherty, Umbral Calculus and the Boustrophedon Transform, 2013.

FORMULA

For n>2, a(n) = A001250(n) - A001250(n-1)/2 = A001250(n) - A000111(n).

a(n) = 2*A000111(n+1)-A000111(n) [Berry et al., 2013] (but compare A231895). - N. J. A. Sloane, Nov 18 2013

E.g.f: 1+(sec(x)+tan(x)-1)*(sec(x)+tan(x)). - Sergei N. Gladkovskii, Nov 07 2014

EXAMPLE

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 + ...

MAPLE

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

CROSSREFS

Cf. A000111, A104854, A001250.

Sequence in context: A102206 A192856 A110886 * A226061 A294197 A030495

Adjacent sequences:  A104851 A104852 A104853 * A104855 A104856 A104857

KEYWORD

nonn

AUTHOR

Michel Criton (mcriton(AT)wanadoo.fr), Apr 23 2005 and May 29 2005

EXTENSIONS

More terms from R. J. Mathar, Feb 14 2008

STATUS

approved

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Last modified March 26 05:43 EDT 2019. Contains 321481 sequences. (Running on oeis4.)