|
%I #12 Mar 04 2013 06:05:38
%S 0,0,0,0,0,0,1,6,21,56,126,252,456,756,1161,1666,2247,2856,3431,3906,
%T 4221,4332,4221,3906,3431,2856,2247,1666,1161,756,456,252,126,56,21,6,
%U 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
%N Number of times a point sum n is attained in all 6^6 permutations of throwing 6 dice.
%C 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.
%C The sixth row of A063260. - _R. J. Mathar_, Aug 27 2008
%H Zhizhang Shen and Christian M. Marston, <a href="http://dx.doi.org/10.1016/0096-3003(95)00062-3">A study of a dice problem</a>, Appl. Math. Comp. vol. 73 iss. 2-3 (1995) 231-247 [<a href="http://www.ams.org/mathscinet-getitem?mr=1366943">MathSciNet</a>] [<a href="http://www.zentralblatt-math.org/zmath/en/advanced/?q=an:0839.05007">Zbl</a>]. [From _R. J. Mathar_, Sep 04 2008, Sep 06 2008]
%F O.g.f.: (1+x+x^2+x^3+x^4+x^5+x^6)^6. - _R. J. Mathar_, Aug 27 2008
%F a(n) = 0 for n > 36.
%o (PARI) v=Vec(('c0+(sum(k=1,6,x^k))^6+O(x^66))); v[1]-='c0; v /* _Joerg Arndt_, Mar 04 2013 */
%Y Cf. A019500.
%Y A056150 gives sums for 3 dice.
%Y A166322 gives sums for 7 dice.
%Y A063260 gives the sums for 2 dice through to 6 dice.
%K nonn
%O 0,8
%A Zdenek Hrubec (zhrubec(AT)yahoo.com), Aug 17 2008
%E Edited by _N. J. A. Sloane_, Jan 17 2009
|
