A258588 Minimal most likely sum for a roll of n 10-sided dice.

1, 11, 16, 22, 27, 33, 38, 44, 49, 55, 60, 66, 71, 77, 82, 88, 93, 99, 104, 110, 115, 121, 126, 132, 137, 143, 148, 154, 159, 165, 170, 176, 181, 187, 192, 198, 203, 209, 214, 220, 225, 231, 236, 242, 247, 253, 258, 264, 269, 275

Offset

1,2

Links

Table of n, a(n) for n=1..50.

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

Formula

G.f.: x*(1 + 10*x + 4*x^2 - 4*x^3)/((1 - x)^2*(1 + x)).

a(n) = floor(11*n/2) = (22*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.

Example

For n=1, there are ten equally likely outcomes, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and the smallest of these is 1, so a(1)=1.

Mathematica

Join[{1}, Table[(22 n + (-1)^n - 1)/4, {n, 2, 50}]]

Prog

(PARI) a(n)=if(n<2, 1, 11*n\2);
vector(50, n, a(n))

Crossrefs

Cf. A030123, A256680, A263941.

Sequence in context: A329389 A227080 A131858 * A371187 A110031 A166451

Adjacent sequences: A258585 A258586 A258587 * A258589 A258590 A258591

Keyword

nonn,easy

Author

Gianmarco Giordano, Nov 06 2015

Status

approved