A204026 Symmetric matrix based on f(i,j)=min(F(i+1),F(j+1)), where F=A000045 (Fibonacci numbers), by antidiagonals.

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

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: A348041 A003983 A087062 * A300119 A323211 A110537

Adjacent sequences: A204023 A204024 A204025 * A204027 A204028 A204029

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 11 2012

Status

approved