A263941 - OEIS

%I #8 Oct 31 2015 05:18:17

%S 1,9,13,18,22,27,31,36,40,45,49,54,58,63,67,72,76,81,85,90,94,99,103,

%T 108,112,117,121,126,130,135,139,144,148,153,157,162,166,171,175,180,

%U 184,189,193,198,202,207,211,216,220,225

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

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

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

%F a(n) = floor(9*n/2) = (18*n + (-1)^n - 1)/4 with n>1, a(1)=1.

%F a(n) = a(n-1) + a(n-2) - a(n-3) for n>4.

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

%e 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.

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

%o (PARI) a(n)=if(n<2,1,9*n\2);

%o vector(50,n,a(n))

%Y Cf. A030123, A130877, A256680.

%K nonn,easy

%O 1,2

%A _Gianmarco Giordano_, Oct 30 2015

%E Edited by _Bruno Berselli_, Oct 30 2015