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 A204173 Symmetric matrix based on f(i,j)=(2i-1 if max(i,j) is odd, and 0 otherwise), by antidiagonals. 2
 1, 0, 0, 2, 0, 2, 0, 2, 2, 0, 3, 0, 2, 0, 3, 0, 3, 0, 0, 3, 0, 4, 0, 3, 0, 3, 0, 4, 0, 4, 0, 3, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 4, 0, 5, 0, 5, 0, 4, 0, 0, 4, 0, 5, 0, 6, 0, 5, 0, 4, 0, 4, 0, 5, 0, 6, 0, 6, 0, 5, 0, 4, 4, 0, 5, 0, 6, 0, 7, 0, 6, 0, 5, 0, 4, 0, 5, 0, 6, 0, 7, 0, 7, 0, 6, 0, 5, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS A204173 represents the matrix M given by f(i,j)=(2i-1 if max(i,j) is odd, and 0 otherwise) for i>=1 and j>=1.  See A204174 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 0 2 0 3 0 4 0 0 0 2 0 3 0 4 0 2 2 2 0 3 0 4 0 0 0 0 0 3 0 4 0 3 3 3 3 3 0 4 0 MATHEMATICA f[i_, j_] := If[Mod[Max[i, j], 2] == 1, (1 + Max[i, j])/2, 0] m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}] TableForm[m[8]] (* 8x8 principal submatrix *) Flatten[Table[f[i, n + 1 - i],   {n, 1, 15}, {i, 1, n}]]  (* A204173 *) 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[%]                 (* A204174 *) TableForm[Table[c[n], {n, 1, 10}]] CROSSREFS Cf. A204174, A204016, A202453. Sequence in context: A309937 A116127 A039979 * A103668 A276812 A246721 Adjacent sequences:  A204170 A204171 A204172 * A204174 A204175 A204176 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jan 12 2012 STATUS approved

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Last modified January 28 07:04 EST 2020. Contains 331317 sequences. (Running on oeis4.)