A002468 - OEIS

A002468

The game of Mousetrap with n cards: the number of permutations of n cards having at least one hit after 2.
(Formerly M2945 N1186)

0, 0, 1, 3, 13, 65, 397, 2819, 22831, 207605, 2094121, 23205383, 280224451, 3662810249, 51523391965, 776082247979, 12463259986087, 212573743211549, 3837628837381201, 73108996989052175, 1465703611456618891, 30847249002794047793, 679998362512214208901, 15668677914172813691699, 376683592679293811722735

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

The subsequence of primes begins: 3, 13, 397, 2819, no more through a(19). - Jonathan Vos Post, Feb 01 2011

REFERENCES

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

Joerg Arndt, Table of n, a(n) for n = 1..102

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.

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) = A001563(n) - A002469(n+2). (corrected by Sean A. Irvine and Joerg Arndt, Feb 10 2014)

MATHEMATICA

a[n_] := (n-2)*(n-2)!-(n-4)*Subfactorial[n-3]-(n-3)*Subfactorial[n-2]; a[1]=a[2]=0; a[3]=1; Table[a[n], {n, 1, 21}] (* Jean-François Alcover, Dec 12 2014 *)

CROSSREFS

Cf. A002467, A002468, A002469, A028306, etc.

Sequence in context: A009102 A080227 A199143 * A198663 A156181 A260783

Adjacent sequences: A002465 A002466 A002467 * A002469 A002470 A002471

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

Added two more terms, Joerg Arndt, Feb 15 2014

STATUS

approved