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

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

Offset: 0

Author

Eric W. Weisstein

Keywords

• nonn
• easy

Comments

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000 (corrected by Sean A. Irvine, Jan 18 2019)
• Eric Weisstein's World of Mathematics, Dice.
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A047355.

Programs

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

Maple

A030123:=n->floor(7*n/2): seq(A030123(n), n=2..100); # Wesley Ivan Hurt, Jan 23 2017

Mathematica

CoefficientList[Series[-(3 x^2 - 3 x - 7)/((x - 1)^2 (x + 1)), {x, 0, 60}], x] (* Vincenzo Librandi, Oct 19 2013 *)

PARI

a(n)=7*n\2 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = floor(7*n/2) for n >= 2.

From Colin Barker, Jun 09 2013: (Start)

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)

Extensions

a(0) and a(1) added by Dmitry Kamenetsky, Nov 03 2017