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%I #14 Nov 07 2015 03:18:48
%S 1,13,19,26,32,39,45,52,58,65,71,78,84,91,97,104,110,117,123,130,136,
%T 143,149,156,162,169,175,182,188,195,201,208,214,221,227,234,240,247,
%U 253,260,266,273,279,286,292,299,305,312,318,325,331,338,344,351,357
%N Minimal most likely sum for a roll of n 12-sided dice.
%H Colin Barker, <a href="/A258589/b258589.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F a(n) = floor(13*n/2) = (26*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 G.f.: -x*(5*x^3-5*x^2-12*x-1) / ((x-1)^2*(x+1)). - _Colin Barker_, Nov 06 2015
%e 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.
%t Join[{1}, Table[(26 n + (-1)^n - 1)/4, {n, 2, 50}]]
%o (PARI) a(n)=if(n<2, 1, 13*n\2);
%o vector(50, n, a(n))
%o (PARI) a(n) = if(n<2,n, (26*n + (-1)^n - 1)/4);
%o vector(50, n, a(n))
%o (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
%Y Cf. A030123, A256680, A263941, A258588.
%K nonn,easy
%O 1,2
%A _Gianmarco Giordano_, Nov 06 2015
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