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

1,3

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

Table of n, a(n) for n=1..69.

Wikipedia, Hankel matrix

Prog

(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

Crossrefs

Cf. A350330, A350348, A350349.

Sequence in context: A286107 A285735 A038810 * A178503 A211275 A240542

Adjacent sequences: A350347 A350348 A350349 * A350351 A350352 A350353

Keyword

nonn

Author

Pontus von Brömssen, Dec 26 2021

Status

approved