A056150 - OEIS

%I #11 Dec 17 2014 16:37:12

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

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

%C The 3rd row of A063260. - _Michel Marcus_, Mar 04 2013

%e 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.

%t Transpose[Tally[Total/@Tuples[Range[6],{3}]]][[2]] (* _Harvey P. Dale_, Dec 17 2014 *)

%o (PARI) Vec(((sum(k=1,6,x^k))^3+O(x^66))) /* _Joerg Arndt_, Mar 04 2013 */

%Y A108907 gives sums for 6 dice.

%Y A166322 gives sums for 7 dice.

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

%K nonn,fini,full

%O 3,2

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

%E Corrected by _Rick L. Shepherd_, May 24 2002