cp's OEIS Frontend

A093658 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)^2,M(n)]], with M(0) = [1].

%I A093658 #6 Oct 24 2017 12:56:33
%S A093658 1,1,1,1,0,1,2,1,1,1,1,0,0,0,1,2,1,0,0,1,1,2,0,1,0,1,0,1,6,2,2,1,2,1,
%T A093658 1,1,1,0,0,0,0,0,0,0,1,2,1,0,0,0,0,0,0,1,1,2,0,1,0,0,0,0,0,1,0,1,6,2,
%U A093658 2,1,0,0,0,0,2,1,1,1,2,0,0,0,1,0,0,0,1,0,0,0,1,6,2,0,0,2,1,0,0,2,1,0,0,1,1
%N A093658 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)^2,M(n)]], with M(0) = [1].
%C A093658 Related to factorials, the incomplete gamma function (A010842) and the total number of arrangements of sets (A000522).
%C A093658 First column forms A093659, where A093659(2^n) = n! for n>=0.
%C A093658 Row sums form A093660, where A093660(2^n) = A000522(n) for n>=0.
%C A093658 Partial sums of the row sums form A093661, where A093661(2^n) = A010842(n) for n>=0.
%F A093658 T(2^n, 1) = n! for n>=0.
%e A093658 Let M(n) be the lower triangular matrix formed from the first 2^n rows.
%e A093658 To generate M(3) from M(2), take the matrix square of M(2):
%e A093658 [1,0,0,0]^2=[1,0,0,0]
%e A093658 [1,1,0,0]...[2,1,0,0]
%e A093658 [1,0,1,0]...[2,0,1,0]
%e A093658 [2,1,1,1]...[6,2,2,1]
%e A093658 and append M(2)^2 to the bottom left corner and M(2) to the bottom right:
%e A093658 [1],
%e A093658 [1,1],
%e A093658 [1,0,1],
%e A093658 [2,1,1,1],
%e A093658 .........
%e A093658 [1,0,0,0],[1],
%e A093658 [2,1,0,0],[1,1],
%e A093658 [2,0,1,0],[1,0,1],
%e A093658 [6,2,2,1],[2,1,1,1].
%e A093658 Repeating this process converges to triangle A093658.
%Y A093658 Cf. A000522, A010842, A093655, A093662.
%K A093658 nonn,tabl
%O A093658 1,7
%A A093658 _Paul D. Hanna_, Apr 08 2004