Search: id:A159934
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%I A159934
%S A159934 1,1,1,1,1,2,0,1,2,2,1,0,2,2,3,2,1,0,2,3,2,1,2,2,0,3,2,4,1,1,
%T A159934 4,2,0,2,4,2,3,1,2,4,3,0,4,2,4,4,3,2,2,6,2,0,2,4,3,2,4,6,2,
%U A159934 3,4,4,0,4,3,4
%V A159934 1,1,1,-1,1,2,0,-1,2,2,-1,0,-2,2,3,2,-1,0,-2,3,2,-1,2,-2,0,-3,2,4,-1,-1,
%W A159934 4,-2,0,-2,4,2,3,-1,-2,4,-3,0,-4,2,4,-4,3,-2,-2,6,-2,0,-2,4,3,2,-4,6,-2,
%X A159934 -3,4,-4,0,-4,3,4
%N A159934 Triangle, row sums = d(n): M * Q; where M = an infinite lower Toeplitz 
               matrix with A159933 in every column. Q = an infinite lower triangular 
               matrix with d(n) shifted: (1, 1, 2, 2, 3, 2, 4,...) as the main diagonal 
               and the rest zeros.
%C A159934 Triangle = an infinite lower triangular Toeplitz matrix with the INVERTi
%C A159934 transform of d(n) in every column; i.e. A159933: (1, 1, -1, 0, -1, 2, 
               -1,...). Row sums of the resulting eigentriangle of d(n) = d(n).
%C A159934 Sum of n-th row terms = rightmost term of next row.
%C A159934 Right border = d(n) shifted.
%e A159934 First few rows of the triangle =
%e A159934 1;
%e A159934 1, 1;
%e A159934 -1, 1, 2;
%e A159934 0, -1, -2, 2;
%e A159934 -1, 0, -2, 2, 3;
%e A159934 2, -1, 0, -2, 3, 2;
%e A159934 -1, 2, -2, 0, -3, 2, 4;
%e A159934 -1, -1, 4, -2, 0, -2, 4, 2;
%e A159934 3, -1, -2, 4, -3, 0, -4, 2, 4;
%e A159934 -4, 3, -2, -2, 6, -2, 0, -2, 4, 3;
%e A159934 2, -4, 6, -2, -3, 4, -4, 0, -4, 3, 4;
%e A159934 2, 2, -8, 6, -3, -2, 8, -2, 0, -3, 4, 2;
%e A159934 -3, 2, 4, -8, 9, -2, -4, 4, -4, 0, -4, 2, 6;
%e A159934 0, -3, 4, 4, -12, 6, -4, -2, 8, -3, 0, -2, 6, 2;
%e A159934 0, 0, -6, 4, 6, -8, 12, -2, -4, 6, -4, 0, -6, 2, 4;
%e A159934 6, 0, 0, -6, 6, 4, -16, 6, -4, -3, 8, -2, 0, -2, 4, 4;
%e A159934 ...
%e A159934 Example: row 6 = (2, -1, 0, -2, 3, 2) = termwise products of
%e A159934 (2, -1, 0, -1, 1, 1) and (1, 1, 2, 2, 3, 2); with dot product sum = 4 
               = d(6).
%Y A159934 A159933
%Y A159934 Sequence in context: A110249 A160756 A145462 this_sequence A067460 A159855 
               A128256
%Y A159934 Adjacent sequences: A159931 A159932 A159933 this_sequence A159935 A159936 
               A159937
%K A159934 tabl,sign
%O A159934 1,6
%A A159934 Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 26 2009

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