A373724 Number of totally positive 3 X 3 matrices having all terms in {1,...,n}.
1, 61, 797, 6490, 32744, 146441, 492277, 1521123, 4105795, 10194558, 22922408, 49594408, 98935110, 190221734, 350417949, 621178227, 1058404994, 1764873413, 2845696865, 4506618651, 6966717779, 10552756376, 15670141644, 22984055065, 33094853060, 47016605050, 65934960254, 91414399149
Offset: 1
Keywords
Links
- Robin Visser, Table of n, a(n) for n = 1..40
Programs
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Mathematica
ispositive2[M_]:=ispositive1[M]=Union@Table[Select[Union@Flatten@Minors[M,r],(#<= 0)&]=={},{r,1,Length[M]}]=={True}; 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]; Table[Length@Select[W[n],ispositive2[#]&],{n,1,6}] -
Sage
import itertools def a(n): ans, W = 0, itertools.product(range(1,n+1), repeat=9) for w in W: M = Matrix(ZZ, 3, 3, w) if (min(M.minors(2)) >= 0) and (M.det() >= 0): ans += 1 return ans # Robin Visser, Apr 18 2025
Extensions
More terms from Robin Visser, Apr 18 2025
Comments