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 A204022 Symmetric matrix based on f(i,j)=max(2i-1, 2j-1), by antidiagonals. 3
 1, 3, 3, 5, 3, 5, 7, 5, 5, 7, 9, 7, 5, 7, 9, 11, 9, 7, 7, 9, 11, 13, 11, 9, 7, 9, 11, 13, 15, 13, 11, 9, 9, 11, 13, 15, 17, 15, 13, 11, 9, 11, 13, 15, 17, 19, 17, 15, 13, 11, 11, 13, 15, 17, 19, 21, 19, 17, 15, 13, 11, 13, 15, 17, 19, 21, 23, 21, 19, 17, 15, 13, 13, 15, 17 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A204022 represents the matrix M given by f(i,j)=max(2i-1,2j-1) for i>=1 and j>=1.  See A204023 for characteristic polynomials of principal submatrices of M, with interlacing zeros.  See A204016 for a guide to other choices of M. LINKS EXAMPLE Northwest corner: 1 3 5 7 9 3 3 5 7 9 5 5 5 7 9 7 7 7 7 9 9 9 9 9 9 MATHEMATICA f[i_, j_] := Max[2 i - 1, 2 j - 1]; m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}] TableForm[m[6]] (* 6x6 principal submatrix *) Flatten[Table[f[i, n + 1 - i],   {n, 1, 15}, {i, 1, n}]]          (* A204022 *) p[n_] := CharacteristicPolynomial[m[n], x]; c[n_] := CoefficientList[p[n], x] TableForm[Flatten[Table[p[n], {n, 1, 10}]]] Table[c[n], {n, 1, 12}] Flatten[%]                         (* A204023 *) TableForm[Table[c[n], {n, 1, 10}]] CROSSREFS Cf. A204022, A204016, A202453. Sequence in context: A158894 A131919 A185154 * A131832 A255316 A078587 Adjacent sequences:  A204019 A204020 A204021 * A204023 A204024 A204025 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jan 11 2012 STATUS approved

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