A263941 Minimal most likely sum for a roll of n 8-sided dice.

1, 9, 13, 18, 22, 27, 31, 36, 40, 45, 49, 54, 58, 63, 67, 72, 76, 81, 85, 90, 94, 99, 103, 108, 112, 117, 121, 126, 130, 135, 139, 144, 148, 153, 157, 162, 166, 171, 175, 180, 184, 189, 193, 198, 202, 207, 211, 216, 220, 225

Offset

1,2

Links

Table of n, a(n) for n=1..50.

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

Formula

G.f.: x*(1 + 8*x + 3*x^2 - 3*x^3)/((1 - x)^2*(1 + x)).

a(n) = floor(9*n/2) = (18*n + (-1)^n - 1)/4 with n>1, a(1)=1.

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

a(n) = -A130877(-n+1) for n>1.

Example

For n=1, there are eight equally likely outcomes, 1,2,3,4,5,6,7,8 and the smallest of these is 1, so a(1)=1.

Mathematica

Join[{1}, Table[(18 n + (-1)^n - 1)/4, {n, 2, 50}]]

Prog

(PARI) a(n)=if(n<2, 1, 9*n\2);
vector(50, n, a(n))

Crossrefs

Cf. A030123, A130877, A256680.

Sequence in context: A211429 A103152 A295113 * A090415 A026283 A307287

Adjacent sequences: A263938 A263939 A263940 * A263942 A263943 A263944

Keyword

nonn,easy

Author

Gianmarco Giordano, Oct 30 2015

Extensions

Edited by Bruno Berselli, Oct 30 2015

Status

approved