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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

%I

%S 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,

%T 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,

%U 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

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

%C 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.

%e Northwest corner:

%e 1 1 1 1 1 1

%e 1 2 2 2 2 2

%e 1 2 3 3 3 3

%e 1 2 3 5 5 5

%e 1 2 3 5 8 8

%e 1 2 3 5 8 13

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

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

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

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

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

%t p[n_] := CharacteristicPolynomial[m[n], x];

%t c[n_] := CoefficientList[p[n], x]

%t TableForm[Flatten[Table[p[n], {n, 1, 10}]]]

%t Table[c[n], {n, 1, 12}]

%t Flatten[%] (* A204027 *)

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

%Y Cf. A204026, A204016, A202453.

%K nonn,tabl

%O 1,5

%A _Clark Kimberling_, Jan 11 2012

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Last modified February 27 03:50 EST 2020. Contains 332299 sequences. (Running on oeis4.)