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A172972 Subtraction triangle based on A029826: c(n)=Product[A029826(i),{i,0,n)];t(n,m)=c(n)-c(m)-c(n-m).

%I A172972 #4 Jun 02 2025 02:40:39
%S A172972 -1,-1,-1,-1,-3,-1,-1,-1,-1,-1,-1,0,2,0,-1,-1,-1,2,2,-1,-1,-1,-1,1,2,
%T A172972 1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,0,1,1,-1,-1,-1,-1,1,1,0,0,1,1,
%U A172972 -1,-1,-1,-1,1,1,0,0,0,1,1,-1,-1
%N A172972 Subtraction triangle based on A029826: c(n)=Product[A029826(i),{i,0,n)];t(n,m)=c(n)-c(m)-c(n-m).
%C A172972 Row sums are:
%C A172972 {-1, -2, -5, -4, 0, 0, 0, 0, 0, 0, 0,...}.
%F A172972 c(n)=Product[A029826(i),{i,0,n)];
%F A172972 t(n,m)=c(n)-c(m)-c(n-m)
%e A172972 {-1},
%e A172972 {-1, -1},
%e A172972 {-1, -3, -1},
%e A172972 {-1, -1, -1, -1},
%e A172972 {-1, 0, 2, 0, -1},
%e A172972 {-1, -1, 2, 2, -1, -1},
%e A172972 {-1, -1, 1, 2, 1, -1, -1},
%e A172972 {-1, -1, 1, 1, 1, 1, -1, -1},
%e A172972 {-1, -1, 1, 1, 0, 1, 1, -1, -1},
%e A172972 {-1, -1, 1, 1, 0, 0, 1, 1, -1, -1},
%e A172972 {-1, -1, 1, 1, 0, 0, 0, 1, 1, -1, -1}
%t A172972 (*A029826 Inverse of Salem polynomial : 1/(x^10 + x^9 - x^7 - x^6 - x^5 - x^4 - x^3 + x + 1).*)
%t A172972 p[x_] = (x^(10) + x^9 - x^7 - x^6 - x^5 - x^4 - x^3 + x + 1); q[ x_] = Expand[x^10*p[1/x]]; a = Table[SeriesCoefficient[Series[1/ q[x], {x, 0, 100}], n], {n, 0, 100}];
%t A172972 c[n_] := Product[a[[m]], {m, 1, n}];
%t A172972 t[n_, m_] := c[n] - (c[m] + c[n - m]);
%t A172972 Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
%t A172972 Flatten[%]
%Y A172972 A029826
%K A172972 sign,tabl,uned
%O A172972 0,5
%A A172972 _Roger L. Bagula_, Feb 06 2010