Search: id:A146973
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%I A146973
%S A146973 1,1,1,2,1,0,2,2,0,1,3,2,0,1,1,3,3,0,2,1,1,4,3,0,2,2,1,2,4,4,
%T A146973 0,3,2,2,2,2,5,4,0,3,3,2,4,2,3,5,5,0,4,3,3,4,4,3,4,6,5,0,4,
%U A146973 4,3,6,4,5,6,6,0,5,4,4,6,6,6,8,5,7
%V A146973 1,-1,1,2,-1,0,-2,2,0,1,3,-2,0,-1,1,-3,3,0,2,-1,1,4,-3,0,-2,2,-1,2,-4,
               4,
%W A146973 0,3,-2,2,-2,2,5,-4,0,-3,3,-2,4,-2,3,-5,5,0,4,-3,3,-4,4,-3,4,6,-5,0,-4,
%X A146973 4,-3,6,-4,5,-6,6,0,5,-4,4,-6,6,-6,8,-5,7
%N A146973 Eigentriangle, row sums = A000931 starting with offset 3.
%C A146973 Row sums and right border = the Padovan sequence, A000931 starting with 
               offset
%C A146973 3: (1, 1, 0, 1, 1, 1, 2, 2, 3,...).
%C A146973 Sum of n-th row terms = rightmost term of next row.
%F A146973 Triangle read by rows, T * Q, where T = an infinite lower triangular 
               matrix with (1, -1, 2, -2, 3, -3,...) in every column and Q = an 
               infinite lower triangular
%F A146973 matrix with the Padovan sequence, A000931 as the main diagonal starting 
               with
%F A146973 offset 3: (1, 1, 0, 1, 1, 1, 2, 2, 3,...). The rest of triangle Q = all 
               zeros.
%F A146973 Triangle A146973 = T * Q.
%e A146973 First few rows of the triangle =
%e A146973 1;
%e A146973 -1, 1;
%e A146973 2, -1, 0;
%e A146973 -2, 2, 0, 1;
%e A146973 3, -2, 0, -1, 1;
%e A146973 -3, 3, 0, 2, -1, 1;
%e A146973 4, -3, 0, -2, 2, -1, 2;
%e A146973 -4, 4, 0, 3, -2, 2, -2, 2;
%e A146973 5, -4, 0, -3, 3, -2, 4, -2, 3;
%e A146973 -5, 5, 0, 4, -3, 3, -4, 4, -3, 4;
%e A146973 6, -5, 0, -4, 4, -3, 6, -4, 6, -4, 5;
%e A146973 -6, 6, 0, 5, -4, 4, -6, 6, -6, 8, -5, 7;
%e A146973 7, -6, 0, -5, 5, -4, 8, -6, 9, -8, 10, -7, 9
%e A146973 -7, 7, 0, 6, -5, 5, -8, 8, -9, 12, -10, 14, -9, 12;
%e A146973 ...
%e A146973 Row 6 = (-2, 2, 0, 1) = termwise products of (-2, 2, 0, 1) and (1, 1, 
               0, 1).
%Y A146973 A000931
%Y A146973 Sequence in context: A003985 A157237 A065676 this_sequence A003263 A157242 
               A135211
%Y A146973 Adjacent sequences: A146970 A146971 A146972 this_sequence A146974 A146975 
               A146976
%K A146973 eigen,tabl,sign
%O A146973 3,4
%A A146973 Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 03 2008

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