A108907 -id:A108907 - cp's OEIS frontend

A056150 Number of combinations for each possible sum when throwing 3 (normal) dice.

1, 3, 6, 10, 15, 21, 25, 27, 27, 25, 21, 15, 10, 6, 3, 1

Offset: 3

Joe Slater (joe(AT)yoyo.cc.monash.edu.au), Aug 05 2000

The 3rd row of A063260. - Michel Marcus, Mar 04 2013

			Using three normal (six-sided) dice we can produce a sum of 3 in just one way: 1,1,1. We can produce a sum of 4 in three ways: 1,1,2; 1,2,1; 2,1,1. We can produce a sum of 5 in 6 ways and so on.

A108907 gives sums for 6 dice.
A166322 gives sums for 7 dice.
A063260 gives the sums for 2 dice through to 6 dice.

Transpose[Tally[Total/@Tuples[Range[6],{3}]]][[2]] (* Harvey P. Dale, Dec 17 2014 *)

Vec(((sum(k=1,6,x^k))^3+O(x^66))) /* Joerg Arndt, Mar 04 2013 */

Corrected by Rick L. Shepherd, May 24 2002

A166322 The number of times a point sum n is attained in all 7^6 permutations of throwing 7 dice.

Original entry on oeis.org

1, 7, 28, 84, 210, 462, 917, 1667, 2807, 4417, 6538, 9142, 12117, 15267, 18327, 20993, 22967, 24017, 24017, 22967, 20993, 18327, 15267, 12117, 9142, 6538, 4417, 2807, 1667, 917, 462, 210, 84, 28, 7, 1

Offset: 7

Robert Goodhand (robert(AT)rgoodhand.fsnet.co.uk), Oct 11 2009

The sum for any number of dice can be obtained by summing the trailing six terms of the sequence above - assuming leading zeros.
1 1 1 1 1 1
1 2 3 4 5 6 5 4 3 2 1
1 3 6 10 15 21 25 27 27 25 21 15 10 6 3 1
1 4 10 20 35 56 80 104 125 140 125 104 80 56 35 20 10 4 1
etc.

Wikipedia, Dice

A056150 gives sums for 3 dice.
A108907 gives sums for 6 dice.
A063260 gives the sums for 2 dice through to 6 dice.

Vec(((sum(k=1,6,x^k))^7+O(x^66))) \\ Joerg Arndt, Mar 04 2013

F_{s,i}(k)= sum(n=0, floor((k-i)/s), (-1)^n*binomial(n,i)*binomial(i-1,k-s*n-1)).

cp's OEIS Frontend

A056150 Number of combinations for each possible sum when throwing 3 (normal) dice.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI

Extensions