cp's OEIS Frontend

A365763 a(n) = number of polynomials of degree 4 in a regular Groebner basis (graded reverse lexicographic order) of n quadratic polynomials in n variables.

%I A365763 #22 Oct 05 2023 14:33:57
%S A365763 0,0,1,3,5,10,14,22,29,39,50,60,76,91,105,126,146,165,189,215,240,264,
%T A365763 297,329,360,390,430,469,507,544,588,635,681,726,770,826,881,935
%N A365763 a(n) = number of polynomials of degree 4 in a regular Groebner basis (graded reverse lexicographic order) of n quadratic polynomials in n variables.
%e A365763 For n=3, the leading monomial is x3^4, so a(3) = 1.
%e A365763 For n=4, the 3 leading monomials are x1x4^3, x2x4^3, x3x4^3, so a(4) = 3.
%o A365763 (Magma)
%o A365763 function a(n);
%o A365763 F:=GF(251);
%o A365763 P<[x]>:=PolynomialRing(F,n,"grevlex");
%o A365763 M2:=[ &*[P| x[i] : i in s] : s in Multisets({1..n},2) ];
%o A365763 A:=[ &+[Random(F)*m : m in M2] : i in [1..n]];
%o A365763 G:=GroebnerBasis(A,4);
%o A365763 return #[ g : g in G | TotalDegree(g) eq 4 ];
%o A365763 end function;
%Y A365763 Cf. A000027 (degree 2), A006463 (degree 3).
%K A365763 nonn,more
%O A365763 1,4
%A A365763 _Gilles Macario-Rat_, Sep 18 2023