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.

0, 0, 1, 3, 5, 10, 14, 22, 29, 39, 50, 60, 76, 91, 105, 126, 146, 165, 189, 215, 240, 264, 297, 329, 360, 390, 430, 469, 507, 544, 588, 635, 681, 726, 770, 826, 881, 935

Offset

1,4

Links

Table of n, a(n) for n=1..38.

Example

For n=3, the leading monomial is x3^4, so a(3) = 1.
For n=4, the 3 leading monomials are x1x4^3, x2x4^3, x3x4^3, so a(4) = 3.

Prog

(Magma)
function a(n);
F:=GF(251);
P<[x]>:=PolynomialRing(F, n, "grevlex");
M2:=[ &*[P| x[i] : i in s] : s in Multisets({1..n}, 2) ];
A:=[ &+[Random(F)*m : m in M2] : i in [1..n]];
G:=GroebnerBasis(A, 4);
return #[ g : g in G | TotalDegree(g) eq 4 ];
end function;

Crossrefs

Cf. A000027 (degree 2), A006463 (degree 3).

Sequence in context: A001841 A266793 A176222 * A008610 A281688 A078411

Adjacent sequences: A365760 A365761 A365762 * A365764 A365765 A365766

Keyword

nonn,more

Author

Gilles Macario-Rat, Sep 18 2023

Status

approved