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 A204030 Symmetric matrix based on f(i,j) = gcd(i+1, j+1), by antidiagonals. 3
 2, 1, 1, 2, 3, 2, 1, 1, 1, 1, 2, 1, 4, 1, 2, 1, 3, 1, 1, 3, 1, 2, 1, 2, 5, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 1, 6, 1, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 7, 2, 1, 2, 1, 2, 1, 3, 1, 5, 3, 1, 1, 3, 5, 1, 3, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A204030 represents the matrix M given by f(i,j) = gcd(i+1, j+1) for i >= 1 and j >= 1. See A204031 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: 2 1 2 1 2 1 2 1 1 3 1 1 3 1 1 3 2 1 4 1 2 1 4 1 1 1 1 5 1 1 1 1 2 3 2 1 6 1 2 3 1 1 1 1 1 7 1 1 MATHEMATICA f[i_, j_] := GCD[i + 1, j + 1]; m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}] TableForm[m[8]] (* 8 X 8 principal submatrix *) Flatten[Table[f[i, n + 1 - i], {n, 1, 15}, {i, 1, n}]] (* A204030 *) 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[%] (* A204111 *) TableForm[Table[c[n], {n, 1, 10}]] CROSSREFS Cf. A204111, A204016, A202453. Sequence in context: A072782 A337014 A122563 * A234503 A333267 A236325 Adjacent sequences: A204027 A204028 A204029 * A204031 A204032 A204033 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jan 11 2012 STATUS approved

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Last modified November 30 04:37 EST 2022. Contains 358431 sequences. (Running on oeis4.)