%I A144218
%S A144218 1,1,1,1,1,2,2,1,2,4,4,2,2,4,9,9,4,4,4,9,21,21,9,8,8,9,21,51,51,21,18,
%T A144218 16,18,21,51,127,127,51,42,36,36,42,51,127,323,323,127,102,84,81,84,102,
%U A144218 127,323,835,835,323,254,204,189,189,204,254,323,835,2188
%N A144218 Eigentriangle, row sums and borders = offset variations of Motzkin numbers
%C A144218 Right border = Motzkin numbers, A001006: (1, 1, 2, 4, 9, 21,...).
%C A144218 Row sums = (1, 2, 4, 9, 21,...);
%C A144218 Left border = A086246: (1, 1, 1, 2, 4, 9, 21,...).Q Sum of n-th row terms 
               = rightmost term of next row.
%F A144218 Let A = an infinite lower triangular matrix with A086246: (1, 1, 1, 2, 
               4, 9, 21, 51,...) in every column; and B = an infinite lower triangular 
               matrix with A001006, (1, 1, 2, 4, 9, 21,...) as the main diagonal 
               and the rest zeros.
%F A144218 a144218 = A*B.
%e A144218 First few rows of the triangle =
%e A144218 1;
%e A144218 1, 1;
%e A144218 1, 1, 2;
%e A144218 2, 1, 2, 4;
%e A144218 4, 2, 2, 4, 9;
%e A144218 9, 4, 4, 4, 9, 21;
%e A144218 21, 9, 8, 8, 9, 21, 51;
%e A144218 51, 21, 18, 16, 18, 21, 51, 127;
%e A144218 127, 51, 42, 36, 36, 42, 51, 127, 323;
%e A144218 323, 127, 102, 84, 81, 84, 102, 127, 323, 835;
%e A144218 835, 323, 254, 204, 189, 189, 204, 254, 835, 2188;
%e A144218 ...
%e A144218 Row 4 = (4, 2, 2, 4, 9) = termwise products of (4, 2, 1, 1, 1) and (1, 
               1, 2, 4, 9) = (4*1, 2*1, 1*2, 1*4, 1*9).
%Y A144218 A001006, Cf. A086246
%Y A144218 Sequence in context: A144963 A035374 A048299 this_sequence A098691 A035364 
               A143808
%Y A144218 Adjacent sequences: A144215 A144216 A144217 this_sequence A144219 A144220 
               A144221
%K A144218 nonn,tabl
%O A144218 0,6
%A A144218 Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 14 2008