keyboard equivalent of dragging the little black square to generate sequence

1. Enter the first number of the sequence

2. Select the range to fill (SHIFT+Down)

3. Use Alt to navigate the menu: Alt+e, i, e, Enter

   This is a shortcut for Edit->Fill->Series

As a mnemonic, adapt the children's song "Old Macdonald," substituting IO (Input/Output) for the Enter key:

Old Macdonald had a series of animals, (alt) E I E IO

The keyboard equivalent to the requested function is placed under the Edit->Fill->Series command in the menu. In newer LibreOffice versions the location is Sheet->Fill Cells->Series....

Before running the command, select the cells to be filled in by using Shift + navigation keys (Shift+Down in the case of OP).

Then you may use mnemonics for running the command. Or even better, set a custom keyboard shortcut via Tools->Customize...->Keyboard. In the dialog, select Category = Edit, Function = Fill Series and set for example Ctrl+Enter as the shortcut.

According to LibreOffice's Help page for Calc there is no keyboard shortcut for that.