A019500 -id:A019500 - cp's OEIS frontend

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

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

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

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