A166322 -id:A166322 - 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

A108907 Number of times a point sum n is attained in all 6^6 permutations of throwing 6 dice.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 6, 21, 56, 126, 252, 456, 756, 1161, 1666, 2247, 2856, 3431, 3906, 4221, 4332, 4221, 3906, 3431, 2856, 2247, 1666, 1161, 756, 456, 252, 126, 56, 21, 6, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Zdenek Hrubec (zhrubec(AT)yahoo.com), Aug 17 2008

nonn

The lowest number that can occur is 6 and the highest is 36 and these can be obtained in only a single combination. The number 7 can occur in 6 different ways: 11-11-12, 11-11-21, 11-12-11, 11-21-11, 12-11-11, 21-11-11, etc.

The sixth row of A063260. - R. J. Mathar, Aug 27 2008

Zhizhang Shen and Christian M. Marston, A study of a dice problem, Appl. Math. Comp. vol. 73 iss. 2-3 (1995) 231-247 [MathSciNet] [Zbl]. [From _R. J. Mathar_, Sep 04 2008, Sep 06 2008]

Cf. A019500.
A056150 gives sums for 3 dice.
A166322 gives sums for 7 dice.
A063260 gives the sums for 2 dice through to 6 dice.

v=Vec(('c0+(sum(k=1,6,x^k))^6+O(x^66)));  v[1]-='c0; v /* Joerg Arndt, Mar 04 2013 */

O.g.f.: (1+x+x^2+x^3+x^4+x^5+x^6)^6. - R. J. Mathar, Aug 27 2008

a(n) = 0 for n > 36.

Edited by N. J. A. Sloane, Jan 17 2009

cp's OEIS Frontend

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

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