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CONCATENATE in ArrayFormula's IF statement in Google Sheets not

Make Google Spreadsheet Formula Repeat Infinitely helped me to expand my formula indefinitely and other StackExchange results helped me get to here:

=ARRAYFORMULA(IF((AF2:AF="")," ","L"&ROW(F2:F)&":AD"&ROW(F2:F)))

However, when I tell "L"&ROW(F2:F)&":AD"&ROW(F2:F) to CONCATENATE, every row gives a results as if it was CONCATENATE(L2:AD2).

I tried =ARRAYFORMULA(IF((AF2:AF="")," ",CONCATENATE("L"&ROW(F2:F)&":AD"&ROW(F2:F)))) and =ARRAYFORMULA(IF((AF2:AF="")," ",CONCATENATE(INDIRECT("L"&ROW(F2:F)&":AD"&ROW(F2:F))))) but neither are working.

I am trying to get each row to CONCATENATE(L2:AD2) then CONCATENATE(L3:AD3) then L4:AD4 and so on.

Any help is most appreciated.

To make more easy to explain and understand by using an example, assume that the source values are in the range A2:C3

Instead of using

ARRAYFORMULA(CONCATENATE(A2:C3)) 

use

ARRAYFORMULA({A2:A3&B2:B3&C2:C3})

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