

A258589


Minimal most likely sum for a roll of n 12sided 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
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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(n1) + a(n2)  a(n3) for n>4.
G.f.: x*(5*x^35*x^212*x1) / ((x1)^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^35*x^212*x1)/((x1)^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



