A350349 Lexicographically earliest increasing sequence of positive integers such that the Hankel matrix of any odd number of consecutive terms is invertible.

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 15, 16, 17, 19, 20, 21, 22, 25, 26, 27, 28, 30, 31, 32, 33, 35, 36, 38, 39, 42, 43, 44, 45, 47, 48, 49, 50, 52, 53, 55, 56, 57, 58, 60, 61, 62, 63, 66, 67, 68, 69, 71, 72, 73, 74, 76, 77, 80, 81, 82, 83, 85, 86, 87, 88, 90

Offset

1,2

Links

Table of n, a(n) for n=1..67.

Wikipedia, Hankel matrix

Prog

(Python)
from sympy import Matrix
from itertools import count
def A350349_list(nmax):
    a=[1]
    for n in range(1, nmax):
        a.append(next(k for k in count(a[-1]+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

Crossrefs

Cf. A350330, A350348, A350350.

Sequence in context: A119930 A173552 A188010 * A008320 A004439 A050126

Adjacent sequences: A350346 A350347 A350348 * A350350 A350351 A350352

Keyword

nonn

Author

Pontus von Brömssen, Dec 26 2021

Status

approved