No spouse No children Yes linear ascendant

Y) Yes. When there is linear ascendant

Heirs are linear ascendant only.

As for the article, Article 889 of the Civil Code set out ((Right of Inheritance of Lineal Ascendant and Sibling)

Article 889 

(1) In the the case where there is no person to become an heir pursuant to the provisions of Article 887, the following persons shall become heirs in accordance with the following order of rank:

(i) lineal ascendants of the decedent; provided that between persons of differing degree of kinship, the person who is of closer relationship shall have higher priority of inheritance;

(ii) siblings of the decedent.

(2) The provisions of paragraph (2) of Article 887 shall apply mutatis mutandis to the case referred to in item (ii) of the preceding paragraph.

The statutory inheritance is shared equally by linear ascendant.

No spouse Children Yes

(Y) Yes.  They have the child.

Article 900 set out the Statutory Share in Inheritance.

Article 900 If there are two or more heirs of the same rank, their shares in inheritance shall be determined by the following items:

( 1)-(3) omitted

( 4) if there are two or more children, lineal ascendants, or siblings, the share in theinheritance of each shall be divided equally; provided that the share in inheritance of an child out of wedlock shall be one half of the share in inheritance of a child in wedlock, and the share in inheritance of a sibling who shares only one parent with the decedent shall be one half of the share in inheritance of a sibling who shares both parents.

In this case,only Child(ren) is/are heir. They share in inheritance eaqually, In addition, although there was a child, if the chihas already passed away, the grandchild will inherit on behalf of the child (art.887 sec2).

As a text, Civil Code 887 (inheritance rights of the child and its transferees) set out the heir.

Article 887

(1) The child of a decedent shall be an heir.

(2) If a decedent’s child has died before the commencement of inheritance, or has lost the right to inheritance by application of the provisions of Article 891 or disinheritance, the child of the decedent’s child shall be an heir as an heir per stirpes; provided that this shall not apply if the child is not a lineal descendant of the decedent.

(3) The provision of the preceding paragraph shall apply mutatis mutandis to the case where an heir per stirpes has died before the commencement of inheritance, or has lost the right of inheritance as an heir per stirpes by application of the provisions of Article 891, or by disinheritance.

The inheritance of legitimate child and child who is not legitimate in the past is equal, although there was a difference in the past (900 Civil Code).