A166556 - OEIS

%I #8 Jul 21 2016 11:39:38

%S 1,2,1,3,1,1,4,2,2,1,5,2,2,1,1,6,3,2,1,2,1,7,3,3,1,3,1,1,8,4,4,2,4,2,

%T 2,1,9,4,4,2,4,2,2,1,1,10,5,4,2,4,2,2,1,2,1,11,5,5,2,4,2,2,1,3,1,1,12,

%U 6,6,3,4,2,2,1,4,2,2,1

%N Triangle read by rows, A000012 * A047999

%F Triangle read by rows, A000012 * A047999; where A000012 = an infinite lower triangular matrix with all 1's: [1; 1,1; 1,1,1;..]; and A047999 = Sierpinski's gasket.

%F The operation takes partial sums of Sierpinski's gasket terms, by columns.

%e First few rows of the triangle =

%e .1;

%e .2, 1;

%e .3, 1, 1;

%e .4, 2, 2, 1;

%e .5, 2, 2, 1, 1;

%e .6, 3, 2, 1, 2, 1;

%e .7, 3, 3, 1, 3, 1, 1;

%e .8, 4, 4, 2, 4, 2, 2, 1;

%e .9, 4, 4, 2, 4, 2, 2, 1, 1;

%e 10, 5, 4, 2, 4, 2, 2, 1, 2, 1;

%e 11, 5, 5, 2, 4, 2, 2, 1, 3, 1, 1;

%e 12, 6, 6, 3, 4, 2, 2, 1, 4, 2, 2, 1;

%e 13, 6, 6, 3, 5, 2, 2, 1, 5, 2, 2, 1, 1;

%e ...

%p A166556 := proc(n,k)

%p     local j;

%p     add(A047999(j,k),j=k..n) ;

%p end proc: # _R. J. Mathar_, Jul 21 2016

%Y Cf. A047999, A006046 (row sums).

%K nonn,easy,tabl

%O 0,2

%A _Gary W. Adamson_, Oct 17 2009