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%I #44 Sep 08 2022 08:44:50
%S 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 84,87,91,94,98,101,105,108,112,115,119,122,126,129,133,136,140,143,
%U 147,150,154,157,161,164,168,171,175,178,182,185,189,192
%N Most likely total for a roll of n 6-sided dice, choosing the smallest if there is a choice.
%C 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 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Dice.html">Dice.</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(7*n/2) for n >= 2.
%F From _Colin Barker_, Jun 09 2013: (Start)
%F a(n) = a(n-1) + a(n-2) - a(n-3) for n >= 5.
%F G.f.: x - x^2 * (3*x^2-3*x-7) / ((x-1)^2*(x+1)). (End)
%p A030123:=n->floor(7*n/2): seq(A030123(n), n=2..100); # _Wesley Ivan Hurt_, Jan 23 2017
%t CoefficientList[Series[-(3 x^2 - 3 x - 7)/((x - 1)^2 (x + 1)), {x, 0, 60}], x] (* _Vincenzo Librandi_, Oct 19 2013 *)
%o (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 (PARI) a(n)=7*n\2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A047355.
%K nonn,easy
%O 0,3
%A _Eric W. Weisstein_
%E a(0) and a(1) added by _Dmitry Kamenetsky_, Nov 03 2017
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