ADVANCED: Copy-Pasting Into Every Other Cell Unique Data

This is something that's been driving me crazy. I work in a library and the following data are accession numbers for old 45 and 78 records. Here's a gross simplification of what I am currently looking at in Excel (the single quotes indicate empty cells) -

2002.400.78.00001
' '
2002.400.78.00002
' '
2002.400.78.00003
' '
2002.400.78.00004
' '
2002.400.78.00005
' '

What I'm trying to do is get the data to look like this -

2002.400.78.00001
2002.400.78.00001
2002.400.78.00002
2002.400.78.00002
2002.400.78.00003
2002.400.78.00003
2002.400.78.00004
2002.400.78.00004
2002.400.78.00005
2002.400.78.00005

To break it down more formulaically I want Excel to copy and paste a given accession number into the blank cells that follow it, until it hits the next accession number at which point I'd like the process to repeat. There are a few cases when accession numbers are separated by more than one blank cell. e.g. -

2002.400.78.00013
' '
' '
' '
2002.400.78.00014
' '
2002.400.78.00015
' '
2002.400.78.00016
' '

Which I would like to see as -

2002.400.78.00013
2002.400.78.00013
2002.400.78.00013
2002.400.78.00013
2002.400.78.00014
2002.400.78.00014
2002.400.78.00015
2002.400.78.00015
2002.400.78.00016
2002.400.78.00016

Any masters out there that could be of assistance? I'm dealing with 12000+ lines of these sorts of data. I've just about thrown the towel in.

If you need more information holler. Much thanks in advance.

Perhaps I don't understand fully, but have you tried pasting everything into one column, and then remove duplicates? You might be left with a single blank cell, but then you can remove that and your data should flow.