%I A140069
%S A140069 1,2,1,4,3,1,8,7,5,1,16,15,17,6,1,32,31,49,23,8,1,64,63,129,72,39,9,1,
%T A140069 128,127,321,201,150,48,11,1,256,255,769,522,501,198,70,12,1,512,511,
%U A140069 1793,1291,1524,699,338,82,14,1,1024,1023,4097,3084,4339,2223,1375,420
%N A140069 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 bidiagonal matrix 
               with [2,1,2,1,2,1,...] and [1,1,1,...] in the subdiagonal.
%C A140069 Sum of n-th row terms = F(2n). Example: sum of 4-th row terms = ( 8 + 
               7 + 5 + 1) = 21 = F(8).
%C A140069 In companion triangle A140068, row sums = odd indexed Fibonacci numbers.
%F A140069 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, 
               with rest zeros. Perform X * [1,0,0,0,...], X * result, etc; with 
               the result of each operation generating successive rows of the triangle.
%e A140069 First few rows of the triangle are:
%e A140069 1;
%e A140069 2, 1;
%e A140069 4, 3, 1;
%e A140069 8, 7, 5, 1;
%e A140069 16, 15, 17, 6, 1;
%e A140069 32, 31, 49, 23, 8, 1;
%e A140069 64, 63, 129, 72, 39, 9, 1;
%e A140069 128, 127, 321, 201, 150, 48, 11, 1;
%e A140069 256, 255, 769, 522, 501, 198, 70, 12, 1;
%e A140069 512, 511, 1793, 1291, 1524, 699, 338, 82, 14, 1;
%e A140069 1024, 1023, 4097, 3084, 4339, 2223, 1375, 420, 110, 15, 1;
%e A140069 ...
%Y A140069 Cf. A140068.
%Y A140069 Sequence in context: A048483 A055248 A103316 this_sequence A105851 A164967 
               A106195
%Y A140069 Adjacent sequences: A140066 A140067 A140068 this_sequence A140070 A140071 
               A140072
%K A140069 nonn,tabl
%O A140069 1,2
%A A140069 Gary W. Adamson and Roger L. Bagula (qntmpkt(AT)yahoo.com), May 04 2008