Counting specific values from same cells over multiple sheets

I am trying to do a count of how many cells equal specific text. I tried to do a COUNTA already, but the cells I'm trying to add have a formula in them so its counting all of them. Also tried to do a COUNTIF, but it was becoming an extremely long formula. I also tried to do a range across multiple worksheets, but couldn't make that work either.

I have attached a sample book, deleted data that is not relevant. In the "SEASON" tab, I want column Y and AR to count if "O" or "D" is found in the cells in each of the other tabs. (There are 21 tabs to count from, I've included three in the sample.)

In each of the tabs not named "SEASON", cells Y6:Y55 and cells AO6:AO55 have a formula which calculates a possible value of "O" or "D" (can also have no value). If those cells have a value of "O" or "D", I want them to be counted in the "SEASON" tab in cells Y6:Y55 and AR6:AR55.

If the formula that is counting is correct the count should be five for all ten numbers that have an "O" or "D" value.

(Sample book removed after solved.)

Create a name for your group of data source sheets. In my attachment I've named sheets 2-4 "Games".

In cell Y6 of the Season sheet use this formula: =SUMPRODUCT(COUNTIF(INDIRECT("'"&Games&"'!Y6"),"O"))+SUMPRODUCT(COUNTIF(INDIRECT("'"&Games&"'!Y6"),"D"))
. . INDIRECT is needed to apply COUNTIF to multiple sheets. SUMPRODUCT is needed to add results for all sheets.
. . Have to essentially duplicate the formula to count both "O" and "D".

Weakness of this solution: the target range (Y6 above) is not a relative cell reference; so the formula won't change when you copy it to other rows --must change the number manually!

[file deleted after solved]

To add to AHS7's suggestion, here is how you would create a list of your sheets so you can give them all a named range...

1st create a range name (I called mine Sheetnanes)
Then put this in the Refers To box: =REPLACE(GET.WORKBOOK(1),1,FIND("]",GET.WORKBOOK(1)),"")

To get a list of sheet names, put this in a cell and copy down (started in A2)...
=IFERROR(INDEX(Sheetnames,ROWS($A$2:A2)),"")
Delete the 1st 3 names (or however many do not apply)
You can then give that list a named range.

A shortened version of AHS7's very good formula would be
=SUMPRODUCT(COUNTIF(INDIRECT("'"&Games&"'!Y"&ROW()),{"O","D"}))
copied down

This will adjust the rows as you copy it down

Happy to help (AHS did the heavy lifting though)