A263941 Minimal most likely sum for a roll of n 8-sided dice.

1, 9, 13, 18, 22, 27, 31, 36, 40, 45, 49, 54, 58, 63, 67, 72, 76, 81, 85, 90, 94, 99, 103, 108, 112, 117, 121, 126, 130, 135, 139, 144, 148, 153, 157, 162, 166, 171, 175, 180, 184, 189, 193, 198, 202, 207, 211, 216, 220, 225

Offset: 1

Author

Gianmarco Giordano, Oct 30 2015

Keywords

• nonn
• easy

Examples

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

Links

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

Crossrefs

Cf. A030123, A130877, A256680.

Programs

Mathematica

Join[{1}, Table[(18 n + (-1)^n - 1)/4, {n, 2, 50}]]

PARI

a(n)=if(n<2,1,9*n\2);
vector(50,n,a(n))

Formula

G.f.: x*(1 + 8*x + 3*x^2 - 3*x^3)/((1 - x)^2*(1 + x)).

a(n) = floor(9*n/2) = (18*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.

a(n) = -A130877(-n+1) for n>1.

Extensions

Edited by Bruno Berselli, Oct 30 2015