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 A204156 Symmetric matrix based on f(i,j)=max(3i-j, 3j-i), by antidiagonals. 3
 1, 4, 4, 7, 3, 7, 10, 6, 6, 10, 13, 9, 5, 9, 13, 16, 12, 8, 8, 12, 16, 19, 15, 11, 7, 11, 15, 19, 22, 18, 14, 10, 10, 14, 18, 22, 25, 21, 17, 13, 9, 13, 17, 21, 25, 28, 24, 20, 16, 12, 12, 16, 20, 24, 28, 31, 27, 23, 19, 15, 11, 15, 19, 23, 27, 31, 34, 30, 26, 22, 18 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A204156 represents the matrix M given by f(i,j)=max(3i-j, 3j-i) for i>=1 and j>=1.  See A204157 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...4...7...10..13 4...3...6...9...12 7...6...5...8...11 10..9...8...7...10 MATHEMATICA f[i_, j_] := -1 + Max[3 i - j, 3 j - i]; 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}]]    (* A204156 *) 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[%]                   (* A204157 *) TableForm[Table[c[n], {n, 1, 10}]] CROSSREFS Cf. A204157, A204016, A202453. Sequence in context: A204158 A053510 A197009 * A163106 A258972 A146564 Adjacent sequences:  A204153 A204154 A204155 * A204157 A204158 A204159 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jan 12 2012 STATUS approved

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Last modified March 20 09:35 EDT 2019. Contains 321345 sequences. (Running on oeis4.)