How to Calculate the 7th Day for `Aqiqah
Question

I had a baby boy born to me on Thursday at 4pm; when should his `Aqiqah be? Should Thursday be counted (in working it out)?
Praise be to Allah.When to offer the `Aqiqah
It is recommended to sacrifice the `Aqiqah on behalf of the newborn on the seventh day, because the Prophet (blessings and peace of Allah be upon him) said: “Every child is in pledge for his `Aqiqah, which should be sacrificed on his behalf on the seventh day, and his head should be shaved and he should be given his name.” (Narrated by Abu Dawud, 2455; classed as authentic by Al-Albani) 
Ibn Qudamah (may Allah have mercy on him) said: 
“Our companions (i.e., scholars from the sa,e school of jurisprudence) said: The Sunnah is to sacrifice it on the seventh day, and we do not know of any difference of opinion among the scholars who say that it is prescribed, that it is recommended to sacrifice it on the seventh day. The evidence for that is the Hadith of Samurah (may Allah be pleased with him), from the Prophet (blessings and peace of Allah be upon him) according to which he said: “Every child is in pledge for his `Aqiqah, which should be sacrificed on his behalf on the seventh day…” (Al-Mughni, 9/364 )
How to calculate the 7th day for `Aqiqah
Once it is established that it is recommended to sacrifice the `Aqiqah on behalf of the child on the seventh day, is the day of birth included in that, according to the majority of scholars? 
An-Nawawi (may Allah have mercy on him) said: “Is the day of birth counted as one of the seven? There are two opinions, the more correct of which is that it is counted, so the sacrifice is done on the sixth day after (the day of birth). 
The second view is that it is not counted, so the sacrifice is done on the seventh day after (the day of birth). This is what is stated in Al-Buwayti, but the first view coincides with the apparent meaning of the Hadiths. If the child is born at night, the day that follows that night is included, and there is no difference of opinion on this point."(Al-Majmu`, 8/411)
In Al-Mawsu`ah Al-Fiqhiyyah (30/279) it says: 
“The majority of jurists are of the view that the day of birth is counted as one of the seven, but the night is not counted if the infant is born at night; rather the day that follows that night is counted.”
Shaykh Ibn `Uthaymin (may Allah have mercy on him) said: 
“The words ‘is to be sacrificed on the seventh day’ mean that it is Sunnah to sacrifice the `Aqiqah on the seventh day. So if the child was born on Saturday, the sacrifice is to be done on Friday, i.e., one day before the day on which the child was born. This is the basic guideline. If the child was born on Thursday, then (the `Aqiqah) should be on Wednesday." (Ash-Sharh Al-Mumti‘, 7/493)
Is the day of birth counted as one of the seven? 
What was said about the day of birth not being counted if the child is born after midday was stated by a number of scholars (may Allah have mercy on them). In fact they said that the day of birth should not be counted at all, whether the child was born before or after midday. This is the view of the Malikis. 
It says in Mukhtasar Khalil: “It is recommended to sacrifice one sheep that meets the requirements of Udhiyah on the seventh day after birth, during the day, and the (previous) day should not be counted if the birth occurred shortly before Fajr.” 
Al-Mawwaq (may Allah have mercy on him) said, quoting from Ibn Rushd: “The view of Ibn Al-Qasim and his report from Malik in Al-Mudawwanah and elsewhere is that if the child was born after dawn, that day is not to be counted, and the seven days should be counted from the following day. If the child is born before dawn, if that was at night, then that day is to be counted." (At-Taj wal Iklil, 4/390)
The correct view is that of the majority of scholars (may Allah have mercy on him), which is that the `Aqiqah is to be sacrificed on the child’s behalf on the seventh day from his birth, because the Prophet (blessings and peace of Allah be upon him) said: “[it] should be sacrificed on his behalf on the seventh day…” 
Shaykh Muhammad ibn Muhammad Al-Mukhtar Ash-Shanqiti (may Allah preserve him) said: “What is meant is that the day of the `Aqiqah is the seventh day after the day of birth. Therefore the day (of the week) on which he is born is the seventh day." (Sharh Al-Mustaqni`) 
The matter is recommended, so if it is possible to sacrifice the `Aqiqah on the seventh day after his birth, this is better, but if it is not possible to do it until after the seventh day, there is nothing wrong with that and the `Aqiqah sacrificed on the child’s behalf will be acceptable. 
An-Nawawi (may Allah have mercy on him) said: “If he sacrifices it after the seventh day or before it, or after the birth, that is acceptable, but if he sacrifices it before the birth, that is not acceptable, and there is no difference of scholarly opinion on this point; rather it is just meat." (Al-Majmu`, 8/411)
And Allah knows best.