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A263941
Minimal most likely sum for a roll of n 8-sided dice.
3
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
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
KEYWORD
nonn,easy
AUTHOR
Gianmarco Giordano, Oct 30 2015
EXTENSIONS
Edited by Bruno Berselli, Oct 30 2015
STATUS
approved