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A204026 Symmetric matrix based on f(i,j)=min(F(i+1),F(j+1)), where F=A000045 (Fibonacci numbers), by antidiagonals. 4
1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 3, 2, 1, 1, 2, 3, 5, 3, 2, 1, 1, 2, 3, 5, 5, 3, 2, 1, 1, 2, 3, 5, 8, 5, 3, 2, 1, 1, 2, 3, 5, 8, 8, 5, 3, 2, 1, 1, 2, 3, 5, 8, 13, 8, 5, 3, 2, 1, 1, 2, 3, 5, 8, 13, 13, 8, 5, 3, 2, 1, 1, 2, 3, 5, 8, 13, 21, 13, 8, 5, 3, 2, 1, 1, 2, 3, 5, 8 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

A204026 represents the matrix M given by f(i,j)=min(F(i+1),F(j+1)) for i>=1 and j>=1.  See A204027 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..96.

EXAMPLE

Northwest corner:

1 1 1 1 1 1

1 2 2 2 2 2

1 2 3 3 3 3

1 2 3 5 5 5

1 2 3 5 8 8

1 2 3 5 8 13

MATHEMATICA

f[i_, j_] := Min[Fibonacci[i + 1], Fibonacci[j + 1]]

m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]

TableForm[m[6]] (* 6x6 principal submatrix *)

Flatten[Table[f[i, n + 1 - i],

  {n, 1, 15}, {i, 1, n}]]  (* A204026 *)

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[%]                 (* A204027 *)

TableForm[Table[c[n], {n, 1, 10}]]

CROSSREFS

Cf. A204026, A204016, A202453.

Sequence in context: A307079 A003983 A087062 * A300119 A323211 A110537

Adjacent sequences:  A204023 A204024 A204025 * A204027 A204028 A204029

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 11 2012

STATUS

approved

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Last modified January 17 23:37 EST 2020. Contains 330995 sequences. (Running on oeis4.)