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 A204006 Symmetric matrix based on f(i,j)=min{2i+j-2,i+2j-2}, by antidiagonals. 3
 1, 2, 2, 3, 4, 3, 4, 5, 5, 4, 5, 6, 7, 6, 5, 6, 7, 8, 8, 7, 6, 7, 8, 9, 10, 9, 8, 7, 8, 9, 10, 11, 11, 10, 9, 8, 9, 10, 11, 12, 13, 12, 11, 10, 9, 10, 11, 12, 13, 14, 14, 13, 12, 11, 10, 11, 12, 13, 14, 15, 16, 15, 14, 13, 12, 11, 12, 13, 14, 15, 16, 17, 17, 16, 15, 14, 13 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A204006 represents the matrix M given by f(i,j)=min{2i+j,i+2j}for i>=1 and j>=1.  See A204007 for characteristic polynomials of principal submatrices of M, with interlacing zeros. LINKS EXAMPLE Northwest corner: 1...2...3...4....5....6 2...4...5...6....7....8 3...5...7...8....9....10 4...6...8...10...11...12 MATHEMATICA f[i_, j_] := Min[2 i + j - 2, 2 j + i - 2]; 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, 12}, {i, 1, n}]]   (* A204006 *) 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[%]                (* A204007 *) TableForm[Table[c[n], {n, 1, 10}]] CROSSREFS Cf. A204007, A202453. Sequence in context: A063712 A340458 A185977 * A106251 A134478 A051162 Adjacent sequences:  A204003 A204004 A204005 * A204007 A204008 A204009 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jan 09 2012 STATUS approved

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Last modified June 12 18:42 EDT 2021. Contains 344959 sequences. (Running on oeis4.)