A061676 - OEIS

%I #3 Mar 30 2012 18:51:34

%S 1,1,1,1,2,1,1,3,3,1,1,4,6,4,1,1,5,10,10,5,1,0,6,15,20,15,6,1,0,5,21,

%T 35,35,21,7,1,0,4,25,56,70,56,28,8,1,0,3,27,80,126,126,84,36,9,1,0,2,

%U 27,104,205,252,210,120,45,10,1,0,1,25,125,305,456,462,330,165,55,11,1

%N Triangle T(n,k) of number of ways of throwing k standard dice to produce a total of n.

%F T(n, k)=T(n-1, k-1)+T(n-2, k-1)+T(n-3, k-1)+T(n-4, k-1)+T(n-5, k-1)+T(n-6, k-1) starting with T(0, 0)=1. T(n, k)=T(7k-n, k); if n>6k or n<k, T(n, k)=0; if n<k+6, T(n, k)=C(n-1, k-1); if n>6k-6, T(n, k)=C(7k-n-1, k-1); T([7k/2], k)=A018901(k).

%e Rows start: 1; 1,1; 1,2,1; 1,3,3,1; 1,4,6,4,1; 1,5,10,10,5,1; 0,6,15,20,15,6,1; 0,5,21,35,35,21,7,1; etc. T(8,2)=5 since 8 =2+6 =3+5 =4+4 =5+3 =6+2.

%Y First 21 terms as A007318 (see formula). Cf. A001592, A069713.

%K nonn,tabl

%O 1,5

%A _Henry Bottomley_, Apr 01 2002