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A350350
Lexicographically earliest nondecreasing sequence of positive integers such that the Hankel matrix of any odd number of consecutive terms is invertible.
3
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.
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
KEYWORD
nonn
AUTHOR
STATUS
approved