A056150 Number of combinations for each possible sum when throwing 3 (normal) dice.

1, 3, 6, 10, 15, 21, 25, 27, 27, 25, 21, 15, 10, 6, 3, 1

Offset: 3

Author

Joe Slater (joe(AT)yoyo.cc.monash.edu.au), Aug 05 2000

Keywords

• nonn
• fini
• full

Comments

The 3rd row of A063260. - Michel Marcus, Mar 04 2013

Examples

			Using three normal (six-sided) dice we can produce a sum of 3 in just one way: 1,1,1. We can produce a sum of 4 in three ways: 1,1,2; 1,2,1; 2,1,1. We can produce a sum of 5 in 6 ways and so on.
		

Crossrefs

A108907 gives sums for 6 dice.

A166322 gives sums for 7 dice.

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

Programs

Mathematica

Transpose[Tally[Total/@Tuples[Range[6],{3}]]][[2]] (* Harvey P. Dale, Dec 17 2014 *)

PARI

Vec(((sum(k=1,6,x^k))^3+O(x^66))) /* Joerg Arndt, Mar 04 2013 */

Extensions

Corrected by Rick L. Shepherd, May 24 2002