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 A204123 Symmetric matrix based on f(i,j)=max([i/j],[j/i]), where [ ]=floor, by antidiagonals. 4
 1, 2, 2, 3, 1, 3, 4, 1, 1, 4, 5, 2, 1, 2, 5, 6, 2, 1, 1, 2, 6, 7, 3, 1, 1, 1, 3, 7, 8, 3, 2, 1, 1, 2, 3, 8, 9, 4, 2, 1, 1, 1, 2, 4, 9, 10, 4, 2, 1, 1, 1, 1, 2, 4, 10, 11, 5, 3, 2, 1, 1, 1, 2, 3, 5, 11, 12, 5, 3, 2, 1, 1, 1, 1, 2, 3, 5, 12, 13, 6, 3, 2, 1, 1, 1, 1, 1, 2, 3, 6, 13, 14, 6, 4, 2 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This sequence represents the matrix M given by f(i,j)=max([i/j],[j/i]) for i>=1 and j>=1.  See A204124 for characteristic polynomials of principal submatrices of M, with interlacing zeros.  See A204016 for a guide to other choices of M. LINKS G. C. Greubel, Table of n, a(n) for the first 100 aintidiagonals EXAMPLE Northwest corner: 1 2 3 4 5 6 2 1 1 2 2 3 3 1 1 1 1 2 4 2 1 1 1 1 5 2 1 1 1 1 6 3 2 1 1 1 MATHEMATICA f[i_, j_] := Max[Floor[i/j], Floor[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}]]  (* A204123 *) 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[%]                 (* A204124 *) TableForm[Table[c[n], {n, 1, 10}]] CROSSREFS Cf. A204124, A204016, A202453. Sequence in context: A162911 A245327 A131821 * A237448 A204143 A143182 Adjacent sequences:  A204120 A204121 A204122 * A204124 A204125 A204126 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jan 11 2012 STATUS approved

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Last modified January 19 09:08 EST 2021. Contains 340267 sequences. (Running on oeis4.)