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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

Table of n, a(n) for n=1..98.

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]] (* 8x8 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: A117358 A294333 A205617 * A186027 A231071 A209156

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 June 20 22:19 EDT 2018. Contains 305615 sequences. (Running on oeis4.)