TIMTOWTDI. A simple analysis demonstrates that there are multiple "optimal" solutions. The first row is dictated (it must contain the 1 ball). The second third and fourth rows are completely determined by choosing one of two alternatives for the second row. The last row has an odd number of balls, thus you can form a symmetrical pattern in that row giving four adjacent pairs of balls between the last two rows, or you can swap two balls of different stripe in the last row giving three adjacent pairs balls between rows and one adjacent pair within the last row.

Four equivalent solutions - very Perlish.