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A258589 Minimal most likely sum for a roll of n 12-sided dice. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A329930 A103804 A063640

Adjacent sequences:  A258586 A258587 A258588 * A258590 A258591 A258592

KEYWORD

nonn,easy

AUTHOR

Gianmarco Giordano, Nov 06 2015

STATUS

approved

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Last modified December 8 14:38 EST 2019. Contains 329865 sequences. (Running on oeis4.)