

A056150


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


2



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

3,2


COMMENTS

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


LINKS

Table of n, a(n) for n=3..18.


EXAMPLE

Using three normal (sixsided) 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.


MATHEMATICA

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


PROG

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


CROSSREFS

A108907 gives sums for 6 dice.
A166322 gives sums for 7 dice.
A063260 gives the sums for 2 dice through to 6 dice.
Sequence in context: A130485 A115015 A231676 * A310081 A240443 A033439
Adjacent sequences: A056147 A056148 A056149 * A056151 A056152 A056153


KEYWORD

nonn,fini,full


AUTHOR

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


EXTENSIONS

Corrected by Rick L. Shepherd, May 24 2002


STATUS

approved



