A018932 The number of permutations of n cards in which 4 will be the next hit after 2.

0, 3, 10, 60, 408, 3120, 26640, 252000, 2620800, 29756160, 366508800, 4869849600, 69455232000, 1058593536000, 17174123366400, 295534407168000, 5377157001216000, 103149354147840000, 2080771454361600000

Offset

4,2

Comments

From the game of Mousetrap.

Links

G. C. Greubel, Table of n, a(n) for n = 4..450

D. J. Mundfrom, A problem of permutations: the Game of "Mousetrap", Eur. J. Combinat. 15 (1994) 555-560.

Formula

a(n) = (n-2)! - 3*(n-3)! + 2*(n-4)! if n > 5. - R. J. Mathar, Oct 02 2008

E.g.f.: (x*(1020 - 1290*x + 340*x^2 - 15*x^3 + 3*x^4) + 60*(17 - 30*x + 15*x^2 - 2*x^3)*log(1-x))/360. - G. C. Greubel, Feb 21 2019

Maple

0, 3, seq((n^2-8*n+17)*factorial(n-4), n=6..30); # Muniru A Asiru, Feb 22 2019

Mathematica

Join[{0, 3}, Table[(n^2-8*n+17)*(n-4)!, {n, 6, 30}]] (* G. C. Greubel, Feb 21 2019 *)

Prog

(PARI) for(n=4, 30, print1(if(n==4, 0, if(n==5, 3, (n^2-8*n+17)*(n-4)!)), ", ")) \\ G. C. Greubel, Feb 21 2019
(Magma) [0, 3] cat [(n^2-8*n+17)*Factorial(n-4): n in [6..30]]; // G. C. Greubel, Feb 21 2019
(Sage) [0, 3] + [(n^2-8*n+17)*factorial(n-4) for n in (6..30)] # G. C. Greubel, Feb 21 2019
(GAP) Concatenation([0, 3], List([6..30], n-> (n^2-8*n+17)*Factorial(n-4) )) # G. C. Greubel, Feb 21 2019

Crossrefs

Cf. A002468.

Sequence in context: A158873 A103591 A245312 * A111562 A009654 A013565

Adjacent sequences: A018929 A018930 A018931 * A018933 A018934 A018935

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Offset changed to 4, more terms, better definition and link from R. J. Mathar, Oct 02 2008

Status

approved