

A108907


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


2



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
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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: 111112, 111121, 111211, 112111, 121111, 211111, 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. 23 (1995) 231247 [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



