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A258589
Minimal most likely sum for a roll of n 12-sided dice.
2
1, 13, 19, 26, 32, 39, 45, 52, 58, 65, 71, 78, 84, 91, 97, 104, 110, 117, 123, 130, 136, 143, 149, 156, 162, 169, 175, 182, 188, 195, 201, 208, 214, 221, 227, 234, 240, 247, 253, 260, 266, 273, 279, 286, 292, 299, 305, 312, 318, 325, 331, 338, 344, 351, 357
OFFSET
1,2
FORMULA
a(n) = floor(13*n/2) = (26*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.
G.f.: -x*(5*x^3-5*x^2-12*x-1) / ((x-1)^2*(x+1)). - Colin Barker, Nov 06 2015
EXAMPLE
For n=1, there are twelve equally likely outcomes, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 and the smallest of these is 1, so a(1)=1.
MATHEMATICA
Join[{1}, Table[(26 n + (-1)^n - 1)/4, {n, 2, 50}]]
PROG
(PARI) a(n)=if(n<2, 1, 13*n\2);
vector(50, n, a(n))
(PARI) a(n) = if(n<2, n, (26*n + (-1)^n - 1)/4);
vector(50, n, a(n))
(PARI) Vec(-x*(5*x^3-5*x^2-12*x-1)/((x-1)^2*(x+1)) + O(x^100)) \\ Colin Barker, Nov 06 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gianmarco Giordano, Nov 06 2015
STATUS
approved