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A030123
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Most likely total for a roll of n 6-sided dice, choosing the smallest if there is a choice.
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7
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0, 1, 7, 10, 14, 17, 21, 24, 28, 31, 35, 38, 42, 45, 49, 52, 56, 59, 63, 66, 70, 73, 77, 80, 84, 87, 91, 94, 98, 101, 105, 108, 112, 115, 119, 122, 126, 129, 133, 136, 140, 143, 147, 150, 154, 157, 161, 164, 168, 171, 175, 178, 182, 185, 189, 192
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OFFSET
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0,3
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COMMENTS
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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
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LINKS
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Eric Weisstein's World of Mathematics, Dice.
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FORMULA
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a(n) = floor(7*n/2) for n >= 2.
a(n) = a(n-1) + a(n-2) - a(n-3) for n >= 5.
G.f.: x - x^2 * (3*x^2-3*x-7) / ((x-1)^2*(x+1)). (End)
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MAPLE
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MATHEMATICA
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CoefficientList[Series[-(3 x^2 - 3 x - 7)/((x - 1)^2 (x + 1)), {x, 0, 60}], x] (* Vincenzo Librandi, Oct 19 2013 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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