AWK how to add all columns beginning with specific row

Question

I have this output:

  Count Process
    238 0
     1 1124027
     1 1124065
     1 1124066
     1 1124069
     1 1124072
     1 1124073
     1 1547365
     1 1547366

I wanted to add all Count except for the first line (238). How do I do this on awk?

so far I have this
awk 'NF == 1 {for (i=2;i<=FNR;++i) sum += i print $i}'
but its an error.

Edit

I am trying to parse the output of this command:

cat /proc/8920/maps | awk '{print$5}' | sort | uniq -c |`awk 'NF == 1 {for (i=2;i<=FNR;++i) sum += i print $i}'` 

Everything works fine until uniq -c, but after that I have problem with awk script to add all lines in first columns except for the first line which is 238. I hope this clears things up.

Hauke Laging's answer and I came up with this script

cat /proc/8920/maps | awk '{print$5}' | sort | uniq -c | awk 'NR>1 { sum+= $1} END  {print sum}'

now its working.

Answer 1

It doesn't make sense to add a value only if it is 1. In that case you can count the matching lines instead:

grep -c " 1 " < inputfile

Real adding is done this way:

awk 'NR>1 { sum+=$1 }; END { print sum }' inputfile