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 A204143 Symmetric matrix based on f(i,j)=max(ceiling(i/j),ceiling(j/i)), by antidiagonals. 3
 1, 2, 2, 3, 1, 3, 4, 2, 2, 4, 5, 2, 1, 2, 5, 6, 3, 2, 2, 3, 6, 7, 3, 2, 1, 2, 3, 7, 8, 4, 2, 2, 2, 2, 4, 8, 9, 4, 3, 2, 1, 2, 3, 4, 9, 10, 5, 3, 2, 2, 2, 2, 3, 5, 10, 11, 5, 3, 2, 2, 1, 2, 2, 3, 5, 11, 12, 6, 4, 3, 2, 2, 2, 2, 3, 4, 6, 12, 13, 6, 4, 3, 2, 2, 1, 2, 2, 3, 4, 6, 13, 14, 7, 4, 3 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A204143 represents the matrix M given by f(i,j)=max(ceiling(i/j),ceiling(j/i)) for i>=1 and j>=1. See A204144 for characteristic polynomials of principal submatrices of M, with interlacing zeros. See A204016 for a guide to other choices of M. LINKS Table of n, a(n) for n=1..95. EXAMPLE Northwest corner: 1 2 3 4 5 6 2 1 2 2 3 3 3 2 1 2 2 2 4 2 2 1 2 2 5 3 2 2 1 2 6 3 2 2 2 1 MATHEMATICA f[i_, j_] := Max[Ceiling[i/j], Ceiling[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}]] (* A204143 *) 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[%] (* A204144 *) TableForm[Table[c[n], {n, 1, 10}]] CROSSREFS Cf. A204144, A204016, A202453. Sequence in context: A360913 A204123 A237448 * A143182 A128715 A237447 Adjacent sequences: A204140 A204141 A204142 * A204144 A204145 A204146 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jan 11 2012 STATUS approved

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Last modified September 18 08:39 EDT 2024. Contains 375997 sequences. (Running on oeis4.)