|
%I #9 May 01 2013 04:06:39
%S 1,1,2,1,0,4,1,2,4,8,1,0,0,0,16,1,2,0,0,16,32,1,0,4,0,16,0,64,1,2,4,8,
%T 16,32,64,128,1,0,0,0,0,0,0,0,256,1,2,0,0,0,0,0,0,256,512,1,0,4,0,0,0,
%U 0,0,256,0,1024
%N Triangle read by rows, Sierpinski's gasket, A047999 * (1,2,4,8,...) diagonalized.
%C Row sums = A001317: (1, 3, 5, 15, 17, 51, 85,...).
%C Number of positive terms in n-th row (n>=0) equals to A000120(n). [From _Vladimir Shevelev_, Oct 25 2010]
%F Triangle read by rows, A047999 * Q. A047999 = Sierpinski's gasket, Q = an infinite lower triangular matrix with (1,2,4,8,...) as the main diagonal and the rest zeros.
%e First few rows of the triangle =
%e 1;
%e 1, 2;
%e 1, 0, 4;
%e 1, 2, 4, 8;
%e 1, 0, 0, 0, 16;
%e 1, 2, 0, 0, 16,.32;
%e 1, 0, 4, 0, 16,..0,..64;
%e 1, 2, 4, 8, 16,.32,..64,..128;
%e 1, 0, 0, 0,..0,..0,...0,....0,..256;
%e 1, 2, 0, 0,..0,..0,...0,....0,..256,...512;
%e 1, 0, 4, 0,..0,..0,...0,....0,..256,.....0,...1024;
%e 1, 2, 4, 8,..0,..0,...0,....0,..256,...512,...l024,...2048;
%e 1, 0, 0, 0, 16,..0,...0,....0,..256,.....0,......0,......0,..4096;
%e ...
%Y Cf. A147999, A001317.
%K nonn,tabl
%O 0,3
%A _Gary W. Adamson_, Oct 17 2009
|
