A258589 Minimal most likely sum for a roll of n 12-sided dice.

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

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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

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

Cf. A030123, A256680, A263941, A258588.

Sequence in context: A058898 A227092 A123840 * A103804 A063640 A092104

Adjacent sequences: A258586 A258587 A258588 * A258590 A258591 A258592

Keyword

nonn,easy

Author

Gianmarco Giordano, Nov 06 2015

Status

approved