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

Author

N. J. A. Sloane

Keywords

• nonn

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.

Crossrefs

Cf. A002468.

Programs

GAP

Concatenation([0,3], List([6..30], n-> (n^2-8*n+17)*Factorial(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

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 *)

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

Sage

[0,3] + [(n^2-8*n+17)*factorial(n-4) for n in (6..30)] # G. C. Greubel, Feb 21 2019

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

Extensions

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