A167271 - OEIS

%I #4 Mar 03 2013 14:17:30

%S 1,1,1,1,0,1,1,2,0,1,1,0,0,0,1,1,3,1,0,0,1,1,0,0,0,0,0,1,1,4,0,3,0,0,

%T 0,1,1,0,1,0,0,0,0,0,1,1,5,0,0,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,1,1,6,

%U 1,6,0,4,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1

%N Triangle read by rows, A167269 columns aerated with k zeros

%C Row sums = A167272: (1, 2, 2, 4, 2, 6, 2, 9,k 3, 8, 2, 19,...).

%C Product of columns = A167273: (1, 1, 3, 4, 10, 13, 28, 37, 73,...).

%F Given triangle A167269, T(n,k), aerate column terms with k zeros.

%e First few rows of the triangle =

%e 1,

%e 1, 1;

%e 1, 0, 1;

%e 1, 2, 0, 1;

%e 1, 0, 0, 0, 1;

%e 1, 3, 1, 0, 0, 1;

%e 1, 0, 0, 0, 0, 0, 1;

%e 1, 4, 0, 3, 0, 0, 0, 1;

%e 1, 0, 1, 0, 0, 0, 0, 0, 1;

%e 1, 5, 0, 0, 1, 0, 0, 0, 0, 1;

%e 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e 1, 6, 1, 6, 0, 4, 0, 0, 0, 0, 0, 1;

%e 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e 1, 7, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1;

%e 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e 1, 8, 0, 10, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 1;

%e ...

%Y Cf. A167269, A167272, A167273

%K nonn,tabl

%O 0,8

%A _Gary W. Adamson_ & _Mats Granvik_, Oct 31 2009