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A256680 Minimal most likely sum for a roll of n 4-sided dice. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A075275 A245270 A123122 * A129189 A066513 A218852

Adjacent sequences:  A256677 A256678 A256679 * A256681 A256682 A256683

KEYWORD

nonn,easy

AUTHOR

Ran Pan, Apr 08 2015

STATUS

approved

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Last modified September 26 06:54 EDT 2017. Contains 292502 sequences.