cp's OEIS Frontend

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

%I A350350 #4 Dec 26 2021 14:15:54
%S A350350 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,
%T A350350 19,21,21,24,24,25,25,26,26,28,28,29,29,30,30,32,32,34,34,35,35,37,37,
%U A350350 38,38,39,39,41,41,43,43,46,46,48,48,50,50,51,51,52,52,55
%N A350350 Lexicographically earliest nondecreasing sequence of positive integers such that the Hankel matrix of any odd number of consecutive terms is invertible.
%C A350350 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.
%H A350350 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hankel_matrix">Hankel matrix</a>
%o A350350 (Python)
%o A350350 from sympy import Matrix
%o A350350 from itertools import count
%o A350350 def A350350_list(nmax):
%o A350350     a=[1]
%o A350350     for n in range(1,nmax):
%o A350350         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))))
%o A350350     return a
%Y A350350 Cf. A350330, A350348, A350349.
%K A350350 nonn
%O A350350 1,3
%A A350350 _Pontus von Brömssen_, Dec 26 2021