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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)
8
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
R. K. Guy and R. J. Nowakowski, Mousetrap, Preprint, Feb 10 1993 [Annotated scanned copy]
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
Sequence in context: A009102 A080227 A199143 * A198663 A156181 A260783
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
Added two more terms, Joerg Arndt, Feb 15 2014
STATUS
approved

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)