A056150 -id:A056150 - 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

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

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

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