A350350 Lexicographically earliest nondecreasing sequence of positive integers such that the Hankel matrix of any odd number of consecutive terms is invertible.

1, 1, 2, 2, 3, 3, 5, 5, 6, 6, 7, 7, 9, 9, 11, 11, 12, 12, 14, 14, 15, 15, 16, 16, 18, 18, 19, 19, 21, 21, 24, 24, 25, 25, 26, 26, 28, 28, 29, 29, 30, 30, 32, 32, 34, 34, 35, 35, 37, 37, 38, 38, 39, 39, 41, 41, 43, 43, 46, 46, 48, 48, 50, 50, 51, 51, 52, 52, 55

Offset: 1

Author

Pontus von Brömssen, Dec 26 2021

Keywords

• nonn

Comments

For 1 <= n <= 34, a(2*n-1) = a(2*n) = 1 + Sum_{k=1..n-1} A350330(k), but this does not hold for n = 35.

Links

• Wikipedia, Hankel matrix

Crossrefs

Cf. A350330, A350348, A350349.

Programs

Python

from sympy import Matrix
from itertools import count
def A350350_list(nmax):
    a=[1]
    for n in range(1,nmax):
        a.append(next(k for k in count(a[-1]) if all(Matrix((n-r)//2+1,(n-r)//2+1,lambda i,j:(a[r:]+[k])[i+j]).det()!=0 for r in range(n-2,-1,-2))))
    return a