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A030123 Most likely total for a roll of n 6-sided dice, choosing the smallest if there is a choice.

%I A030123 #45 Feb 16 2025 08:32:35
%S A030123 0,1,7,10,14,17,21,24,28,31,35,38,42,45,49,52,56,59,63,66,70,73,77,80,
%T A030123 84,87,91,94,98,101,105,108,112,115,119,122,126,129,133,136,140,143,
%U A030123 147,150,154,157,161,164,168,171,175,178,182,185,189,192
%N A030123 Most likely total for a roll of n 6-sided dice, choosing the smallest if there is a choice.
%C A030123 In fact ceiling(7n/2) is just as likely as floor(7n/2), so sequence could equally well be A047345. - _Henry Bottomley_, Jan 19 2001. a(1) is the only exception to this rule. - _Dmitry Kamenetsky_, Nov 03 2017
%H A030123 Vincenzo Librandi, <a href="/A030123/b030123.txt">Table of n, a(n) for n = 0..1000</a> (corrected by Sean A. Irvine, Jan 18 2019)
%H A030123 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Dice.html">Dice.</a>
%H A030123 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A030123 a(n) = floor(7*n/2) for n >= 2.
%F A030123 From _Colin Barker_, Jun 09 2013: (Start)
%F A030123 a(n) = a(n-1) + a(n-2) - a(n-3) for n >= 5.
%F A030123 G.f.: x - x^2 * (3*x^2-3*x-7) / ((x-1)^2*(x+1)). (End)
%p A030123 A030123:=n->floor(7*n/2): seq(A030123(n), n=2..100); # _Wesley Ivan Hurt_, Jan 23 2017
%t A030123 CoefficientList[Series[-(3 x^2 - 3 x - 7)/((x - 1)^2 (x + 1)), {x, 0, 60}], x] (* _Vincenzo Librandi_, Oct 19 2013 *)
%o A030123 (Magma)  I:=[7,10,14]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..60]]; // _Vincenzo Librandi_, Oct 19 2013
%o A030123 (PARI) a(n)=7*n\2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A030123 Cf. A047355.
%K A030123 nonn,easy
%O A030123 0,3
%A A030123 _Eric W. Weisstein_
%E A030123 a(0) and a(1) added by _Dmitry Kamenetsky_, Nov 03 2017