%I A140068
%S A140068 1,1,1,1,3,1,1,7,4,1,1,15,11,6,1,1,31,26,23,7,1,1,63,57,72,30,9,1,1,127,
%T A140068 120,201,102,48,10,1,1,255,247,522,303,198,58,12,1,1,511,502,1291,825,
%U A140068 699,256,82,13,1,1,1023,1013,3084,2116,2223,955,420,95,15,1,1,2047,2036
%N A140068 Triangle read by rows, n-th row = (n-1)-th power of the matrix X * [1,
               0,0,0,...] where X = an infinite lower triangular matrix with [1,
               2,1,2,1,2,...] in the main diagonal and [1,1,1,...] in the subdiagonal.
%C A140068 Sum of n-th row terms = odd indexed Fibonacci numbers, F(2n+1); e.g. 
               sum of row 5 terms = (1 + 15 + 11 + 6 + 1) = 34 = F(9).
%C A140068 The triangle is a companion to A140069 (having row sums = even indexed 
               Fibonacci numbers).
%F A140068 Triangle read by rows, n-th row = (n-1)-th power of the matrix X * [1,
               0,0,0,...] where X = an infinite lower triangular matrix with [1,
               2,1,2,1,2,...] in the main diagonal and [1,1,1,...] in the subdiagonal. 
               Given the matrix X, perform X * [1,0,0,0,...] and then iterate: X 
               * (result), etc. and record the result as each successive row of 
               the triangle.
%e A140068 First few rows of the triangle are:
%e A140068 1;
%e A140068 1, 1;
%e A140068 1, 3, 1;
%e A140068 1, 7, 4, 1;
%e A140068 1, 15, 11, 6, 1;
%e A140068 1, 31, 26, 23, 7, 1;
%e A140068 1, 63, 57, 72, 30, 9, 1;
%e A140068 1, 127, 120, 201, 102, 48, 10, 1;
%e A140068 1, 255, 247, 522, 303, 198, 58, 12, 1;
%e A140068 ...
%Y A140068 Cf. A140069.
%Y A140068 Sequence in context: A135288 A078026 A126713 this_sequence A121300 A128119 
               A158198
%Y A140068 Adjacent sequences: A140065 A140066 A140067 this_sequence A140069 A140070 
               A140071
%K A140068 nonn,tabl
%O A140068 1,5
%A A140068 Gary W. Adamson and Roger L. Bagula (qntmpkt(AT)yahoo.com), May 04 2008