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

0,8

Comments

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

Links

Table of n, a(n) for n=0..78.

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]

Formula

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.

Prog

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

Crossrefs

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.

Sequence in context: A008498 A015640 A138780 * A306940 A120478 A008488

Adjacent sequences: A108904 A108905 A108906 * A108908 A108909 A108910

Keyword

nonn

Author

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

Extensions

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

Status

approved