A204114 - OEIS

A204114

Symmetric matrix based on f(i,j) = gcd(L(i), L(j)), where L=A000032 (Lucas numbers), by antidiagonals.

1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 7, 1, 3, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 4, 1, 1, 18, 1, 1, 4, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 29, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1

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OFFSET

1,5

COMMENTS

A204114 represents the matrix M given by f(i,j) = gcd(L(i+1), L(j+1)) for i >= 1 and j >= 1. See A204115 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 3 1 1 1

1 1 4 1 1

1 1 1 7 1

1 1 1 1 11

MATHEMATICA

u[n_] := LucasL[n]

f[i_, j_] := GCD[u[i], u[j]];