cp's OEIS Frontend

A373724 Number of totally positive 3 X 3 matrices having all terms in {1,...,n}.

%I A373724 #19 Apr 21 2025 02:35:00
%S A373724 1,61,797,6490,32744,146441,492277,1521123,4105795,10194558,22922408,
%T A373724 49594408,98935110,190221734,350417949,621178227,1058404994,
%U A373724 1764873413,2845696865,4506618651,6966717779,10552756376,15670141644,22984055065,33094853060,47016605050,65934960254,91414399149
%N A373724 Number of totally positive 3 X 3 matrices having all terms in {1,...,n}.
%C A373724 A matrix is totally positive if all its minors are nonnegative.
%H A373724 Robin Visser, <a href="/A373724/b373724.txt">Table of n, a(n) for n = 1..40</a>
%t A373724 ispositive2[M_]:=ispositive1[M]=Union@Table[Select[Union@Flatten@Minors[M,r],(#<= 0)&]=={},{r,1,Length[M]}]=={True};
%t A373724 W[n_]:=W[n]=Flatten[Table[{{a11,a12,a13},{a21,a22,a23},{a31,a32,a33}},{a11,1,n},{a12,1,n},{a13,1,n},{a21,1,n},{a22,1,n},{a23,1,n},{a31,1,n},{a32,1,n},{a33,1,n}],8];
%t A373724 Table[Length@Select[W[n],ispositive2[#]&],{n,1,6}]
%o A373724 (Sage)
%o A373724 import itertools
%o A373724 def a(n):
%o A373724     ans, W = 0, itertools.product(range(1,n+1), repeat=9)
%o A373724     for w in W:
%o A373724         M = Matrix(ZZ, 3, 3, w)
%o A373724         if (min(M.minors(2)) >= 0) and (M.det() >= 0): ans += 1
%o A373724     return ans  # _Robin Visser_, Apr 18 2025
%Y A373724 Cf. A211059, A373723.
%K A373724 nonn
%O A373724 1,2
%A A373724 _José María Grau Ribas_, Jun 15 2024
%E A373724 More terms from _Robin Visser_, Apr 18 2025