cp's OEIS Frontend

A093662 Lower triangular matrix, read by rows, defined as the convergent of the concatenation of matrices using the iteration: M(n+1) = [[M(n),0*M(n)],[M(n),M(n)^2]], with M(0) = [1].

%I A093662 #6 Mar 20 2013 06:44:31
%S A093662 1,1,1,1,0,1,1,1,2,1,1,0,0,0,1,1,1,0,0,2,1,1,0,1,0,2,0,1,1,1,2,1,5,2,
%T A093662 4,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,2,1,1,0,1,0,0,0,0,0,2,0,1,1,1,
%U A093662 2,1,0,0,0,0,5,2,4,1,1,0,0,0,1,0,0,0,2,0,0,0,1,1,1,0,0,2,1,0,0,5,2,0,0,4,1
%N A093662 Lower triangular matrix, read by rows, defined as the convergent of the concatenation of matrices using the iteration: M(n+1) = [[M(n),0*M(n)],[M(n),M(n)^2]], with M(0) = [1].
%C A093662 Row sums form A093663, where A093663(2^n) = A016121(n) for n>=0. The 2^n-th row converges to A093664, where A093664(2^n+1) = A016121(n) for n>=0.
%e A093662 Let M(n) be the lower triangular matrix formed from the first 2^n rows.
%e A093662 To generate M(3) from M(2), obtain the matrix square of M(2):
%e A093662 [1,0,0,0]^2=[1,0,0,0]
%e A093662 [1,1,0,0]...[2,1,0,0]
%e A093662 [1,0,1,0]...[2,0,1,0]
%e A093662 [1,1,2,1]...[5,2,4,1],
%e A093662 then M(3) is formed by starting with M(2) and appending M(2) to the bottom left and M(2)^2 to the bottom right:
%e A093662 [1],
%e A093662 [1,1],
%e A093662 [1,0,1],
%e A093662 [1,1,2,1],
%e A093662 ..........
%e A093662 [1,0,0,0],[1],
%e A093662 [1,1,0,0],[2,1],
%e A093662 [1,0,1,0],[2,0,1],
%e A093662 [1,1,2,1],[5,2,4,1].
%e A093662 Repeating this process converges to triangle A093662.
%Y A093662 Cf. A016121, A093655, A093658, A093663, A093664.
%K A093662 nonn,tabl
%O A093662 1,9
%A A093662 _Paul D. Hanna_, Apr 08 2004