%I A140071
%S A140071 1,3,1,9,4,1,27,13,7,1,81,40,34,8,1,243,121,142,42,11,1,729,364,547,184,
%T A140071 75,12,1,2187,1093,2005,731,409,87,15,1,6561,3280,7108,2736,1958,496,
%U A140071 132,16,1,19683,9841,24604,9844,8610,2454,892,148,19,1
%N A140071 Triangle read by rows: iterates of X * [1,0,0,0,...]; where X = an infinite 
               lower bidiagonal matrix with [3,1,3,1,3,1...] in the main diagonal 
               and [1,1,1,...] in the subdiagonal.
%C A140071 Sum of n-th row terms = A007070(n-1): (1, 4, 14, 48, 164, 560, 1912,...).
%C A140071 Companion triangle A140070 uses an analogous operation with the main 
               diagonal [1,3,1,3,1,3,...].
%F A140071 Triangle read by rows: iterates of X * [1,0,0,0,...]; where X = an infinite 
               lower bidiagonal matrix with [3,1,3,1,3,1...] in the main diagonal 
               and [1,1,1,...] in the subdiagonal; with the rest zeros.
%e A140071 First few rows of the triangle are:
%e A140071 1;
%e A140071 3, 1;
%e A140071 9, 4, 1;
%e A140071 27, 13, 7, 1;
%e A140071 81, 40, 34, 8, 1;
%e A140071 243, 121, 142, 42, 11, 1;
%e A140071 729, 364, 547, 184, 75, 12, 1;
%e A140071 2187, 1093, 2005, 731, 409, 87, 15, 1;
%e A140071 6561, 3280, 7108, 2736, 1958, 496, 132, 16, 1;
%e A140071 ...
%Y A140071 Cf. A140070, A007070.
%Y A140071 Sequence in context: A162852 A054448 A106516 this_sequence A067417 A016577 
               A124573
%Y A140071 Adjacent sequences: A140068 A140069 A140070 this_sequence A140072 A140073 
               A140074
%K A140071 nonn,tabl
%O A140071 1,2
%A A140071 Gary W. Adamson and Roger L. Bagula (qntmpkt(AT)yahoo.com), May 04 2008