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 A204112 Symmetric matrix based on f(i,j) = gcd(F(i+1), F(j+1)), where F=A000045 (Fibonacci numbers), by antidiagonals. 3
 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 8, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 2, 1, 5, 2, 1, 1, 2, 5, 1, 2, 1, 1, 1, 3, 1, 1, 1, 21, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS A204112 represents the matrix M given by f(i,j) = gcd(F(i+1), F(j+1)) for i >= 1 and j >= 1.  See A204113 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  1  1  1  1  1   1  2  1  1  2  1   1  1  3  1  1  1   1  1  1  5  1  1   1  2  1  1  8  1   1  1  1  1  1 13 MATHEMATICA u[n_] := Fibonacci[n + 1] f[i_, j_] := GCD[u[i], u[j]]; 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}]]    (* A204112 *) 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[%]                   (* A204113 *) TableForm[Table[c[n], {n, 1, 10}]] CROSSREFS Cf. A204113, A204016, A202453. Sequence in context: A294333 A321125 A205617 * A186027 A322482 A231071 Adjacent sequences:  A204109 A204110 A204111 * A204113 A204114 A204115 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jan 11 2012 STATUS approved

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Last modified July 26 17:37 EDT 2021. Contains 346294 sequences. (Running on oeis4.)