A166322 The number of times a point sum n is attained in all 7^6 permutations of throwing 7 dice.

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

Author

Robert Goodhand (robert(AT)rgoodhand.fsnet.co.uk), Oct 11 2009

Keywords

• nonn
• fini
• full

Comments

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.

Links

• Wikipedia, Dice

Crossrefs

A056150 gives sums for 3 dice.

A108907 gives sums for 6 dice.

A063260 gives the sums for 2 dice through to 6 dice.

Programs

PARI

Vec(((sum(k=1,6,x^k))^7+O(x^66))) \\ Joerg Arndt, Mar 04 2013

Formula

F_{s,i}(k)= sum(n=0, floor((k-i)/s), (-1)^n*binomial(n,i)*binomial(i-1,k-s*n-1)).