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%I A204129 #5 Mar 30 2012 18:58:07
%S A204129 1,1,1,1,3,1,1,1,1,1,1,1,4,1,1,1,1,1,1,1,1,1,1,1,7,1,1,1,1,1,1,1,1,1,
%T A204129 1,1,1,1,1,1,11,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,18,1,1,1,1,1,1,
%U A204129 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,29,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A204129 Symmetric matrix based on f(i,j)=(L(i) if i=j and 1 otherwise), where L=A000032 (Lucas numbers), by antidiagonals.
%C A204129 A204129 represents the matrix M given by f(i,j)=(L(i) if i=j and 1 otherwise) for i>=1 and j>=1.  See A204130 for characteristic polynomials of principal submatrices of M, with interlacing zeros.  See A204016 for a guide to other choices of M.
%e A204129 Northwest corner:
%e A204129 1 1 1 1 1
%e A204129 1 3 1 1 1
%e A204129 1 1 4 1 1
%e A204129 1 1 1 7 1
%e A204129 1 1 1 1 11
%t A204129 f[i_, j_] := 1; f[i_, i_] := LucasL[i];
%t A204129 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204129 TableForm[m[8]] (* 8x8 principal submatrix *)
%t A204129 Flatten[Table[f[i, n + 1 - i],
%t A204129   {n, 1, 15}, {i, 1, n}]]  (* A204129 *)
%t A204129 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204129 c[n_] := CoefficientList[p[n], x]
%t A204129 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204129 Table[c[n], {n, 1, 12}]
%t A204129 Flatten[%]                 (* A204130 *)
%t A204129 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204129 Cf. A204130, A204016, A202453.
%K A204129 nonn,tabl
%O A204129 1,5
%A A204129 _Clark Kimberling_, Jan 11 2012

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