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A030123 Most likely total for a roll of n 6-sided dice, choosing the smallest if there is a choice. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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).

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)

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 *)

PROG

(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

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

CROSSREFS

Cf. A047355.

Sequence in context: A108980 A005526 A192292 * A191833 A020752 A134302

Adjacent sequences:  A030120 A030121 A030122 * A030124 A030125 A030126

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein

EXTENSIONS

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

STATUS

approved

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Last modified June 15 17:43 EDT 2019. Contains 324142 sequences. (Running on oeis4.)