A256680 Minimal most likely sum for a roll of n 4-sided dice.

0, 1, 5, 7, 10, 12, 15, 17, 20, 22, 25, 27, 30, 32, 35, 37, 40, 42, 45, 47, 50, 52, 55, 57, 60, 62, 65, 67, 70, 72, 75, 77, 80, 82, 85, 87, 90, 92, 95, 97, 100, 102, 105, 107, 110, 112, 115, 117, 120, 122, 125, 127, 130, 132, 135, 137, 140, 142, 145, 147, 150, 152, 155, 157, 160, 162

Offset

0,3

Comments

In fact ceiling(5n/2) and floor(5n/2) have the same probability.

a(n) equals A047215(n) except for n=1.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Ran Pan, Exercise G, Project P

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

a(n) = floor(5*n/2), for n>=2; a(0)=0 and a(1)=1.

From Colin Barker, Apr 08 2015: (Start)

a(n) = (-1+(-1)^n+10*n)/4 for n>1.

a(n) = a(n-1)+a(n-2)-a(n-3) for n>4.

G.f.: -x*(x^3-x^2-4*x-1) / ((x-1)^2*(x+1)).

(End)

Example

For n=1, there are four equally likely outcomes, 1,2,3,4, and the smallest of these is 1, so a(1)=1.

Maple

a:= n-> iquo(5*n, 2) -`if`(n=1, 1, 0):
seq(a(n), n=0..80);  # Alois P. Heinz, Apr 08 2015

Mathematica

Join[{0, 1}, Table[Floor[5 n/2], {n, 2, 100}]]

Prog

(Magma) [n le 1 select n else Floor(5*n/2): n in [0..70]]; // Vincenzo Librandi, Apr 08 2015
(PARI) a(n)=if(n<2, n, 5*n\2) \\ Charles R Greathouse IV, Apr 08 2015
(PARI) concat(0, Vec(-x*(x^3-x^2-4*x-1)/((x-1)^2*(x+1)) + O(x^100))) \\ Colin Barker, Apr 08 2015

Crossrefs

Cf. A030123, A047215.

Sequence in context: A245270 A319267 A123122 * A293867 A129189 A066513

Adjacent sequences: A256677 A256678 A256679 * A256681 A256682 A256683

Keyword

nonn,easy

Author

Ran Pan, Apr 08 2015

Status

approved