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A002469 The game of Mousetrap with n cards: the number of permutations of n cards in which 2 is the only hit.
(Formerly M3962 N1635)
8
0, 0, 1, 5, 31, 203, 1501, 12449, 114955, 1171799, 13082617, 158860349, 2085208951, 29427878435, 444413828821, 7151855533913, 122190894996451, 2209057440250799, 42133729714051825, 845553296311189109, 17810791160738752207, 392911423093684031099 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,4

REFERENCES

R. K. Guy, Unsolved Problems Number Theory, E37.

R. K. Guy and R. J. Nowakowski, "Mousetrap," in D. Miklos, V. T. Sos and T. Szonyi, eds., Combinatorics, Paul Erdős is Eighty. Bolyai Society Math. Studies, Vol. 1, pp. 193-206, 1993.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 2..100

R. K. Guy and R. J. Nowakowski, Mousetrap, Preprint, Feb 10 1993 [Annotated scanned copy]

J. Metzger, Email to N. J. A. Sloane, Apr 30 1991

Daniel J. Mundfrom, A problem in permutations: the game of 'Mousetrap'. European J. Combin. 15 (1994), no. 6, 555-560.

M. Z. Spivey, Staircase rook polynomials and Cayley's game of mousetrap, Eur. J. Combinat. 30 (2) (2009) 532-539

A. Steen, Some formulas respecting the game of mousetrap, Quart. J. Pure Applied Math., 15 (1878), 230-241.

Eric Weisstein's World of Mathematics, Mousetrap

FORMULA

a(n) = sum of terms in (n-2)-nd row of triangle A159610; equivalent to: a(n) = (n-2)*A000255(n-1) + A000166(n). -  Gary W. Adamson, Apr 17 2009

a(n) = (n-3)* A000166(n-2) + (n-4)* A000166(n-3). - Gary Detlefs, Apr 10 2010

a(n)= (n-3)*floor(((n-2)!+1)/e) + (n-4)*floor(((n-3)!+1)/e), for n>2. - Gary Detlefs, Apr 10 2010

G.f.: x - 1 + (1-2*x)/(x*Q(0)), where Q(k)= 1/x - (2*k+1) - (k+1)*(k+2)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Apr 25 2013

EXAMPLE

G.f.: x^4 + 5*x^5 + 31*x^6 + 203*x^7 + 1501*x^8 + 12449*x^9 + 114955*x^10 + ...

MAPLE

A002469:=n->(n-3)*floor(((n-2)!+1)/exp(1)) + (n-4)*floor(((n-3)!+1)/exp(1)): 0, seq(A002469(n), n=3..30); # Wesley Ivan Hurt, Jan 10 2017

MATHEMATICA

Join[{0}, Table[(n-3)Floor[((n-2)!+1)/E]+(n-4)Floor[((n-3)!+1)/E], {n, 3, 30}]] (* Harvey P. Dale, Feb 05 2012 *)

a[n_] := (n-3)*Subfactorial[n-2]+(n-4)*Subfactorial[n-3]; a[n_ /; n <= 3] = 0; Table[a[n], {n, 2, 23}] (* Jean-François Alcover, Dec 12 2014 *)

PROG

(PARI)

default(realprecision, 200);

e=exp(1);

A002469(n) = if( n<=3, 0, (n-3)*floor(((n-2)!+1)/e) + (n-4)*floor(((n-3)!+1)/e) );

/* Joerg Arndt, Apr 22 2013 */

CROSSREFS

Cf. A002468, A002467, A028306, A159610, A000255, A000166.

Sequence in context: A260782 A084235 A288688 * A092636 A178792 A007197

Adjacent sequences:  A002466 A002467 A002468 * A002470 A002471 A002472

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Harvey P. Dale, Feb 05 2012

STATUS

approved

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Last modified August 17 13:36 EDT 2017. Contains 290635 sequences.