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A002469
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The game of Mousetrap with n cards.
(Formerly M3962 N1635)
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6
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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; internal format)
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OFFSET
| 2,4
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COMMENTS
| Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 17 2009: (Start)
a(n) = sum of terms in (n-2)-nd row of triangle A159610; equivalent to:
A002469(n) = (n-2)*A000255(n-1) + A000166(n). Example: A002469(4) = 2*A000255(3) + A000166(4) or: 31 = 2*11 + 9. (End)
a(n) = (n-3)* A000166(n-2) + (n-4)* A000166(n-3)..a(5)= 2*2+1 = 5,a(6)=3*9+2*2=31,a(7)=4*44+3*9= 203... [From Gary Detlefs (gdetlefs(AT)aol.com), Apr 10 2010]
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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 Erdos is Eighty. Bolyai Society Math. Studies, Vol. 1, pp. 193-206, 1993.
Mundfrom, Daniel J.; A problem in permutations: the game of `Mousetrap'. European J. Combin. 15 (1994), no. 6, 555-560.
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).
A. Steen, Some formulae respecting the game of mousetrap, Quart. J. Pure Applied Math., 15 (1878), 230-241.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 2..100
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| a(n)= (n-3)*floor(((n-2)!+1)/e) + (n-4)*floor(((n-3)!+1)/e), for n>2 [From Gary Detlefs (gdetlefs(AT)aol.com), Apr 10 2010]
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MATHEMATICA
| Join[{0}, Table[(n-3)Floor[((n-2)!+1)/E]+(n-4)Floor[((n-3)!+1)/E], {n, 3, 30}]] (* From Harvey P. Dale, Feb 05 2012 *)
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CROSSREFS
| Cf. A002468, A002467, A028306, etc.
Cf. A159610, A000255, A000166 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 17 2009]
Sequence in context: A108079 A164038 A084235 * A092636 A178792 A007197
Adjacent sequences: A002466 A002467 A002468 * A002470 A002471 A002472
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KEYWORD
| nonn,nice,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Harvey P. Dale, Feb 05 2012
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