cp's OEIS Frontend

A146973 Eigentriangle, row sums = A000931 starting with offset 3.

%I A146973 #9 Nov 20 2022 10:53:09
%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,
%T A146973 4,0,3,-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,
%U A146973 -4,4,-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 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 matrix with the Padovan sequence, A000931 as the main diagonal starting with offset 3: (1, 1, 0, 1, 1, 1, 2, 2, 3,...). The rest of triangle Q = all zeros. This triangle = 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 Cf. A000931.
%K A146973 eigen,tabl,sign
%O A146973 3,4
%A A146973 _Gary W. Adamson_, Nov 03 2008