* Gas rig count sheds 15 after six-month high last week * Horizontal rigs rise for third time in 4 weeks * Oil rig count up 8 to 1,369, 1st gain in 3 weeks NEW YORK, Sept 20 (Reuters) - The number of rigs drilling for natural gas in the United States slid by 15 this week after posting a six-month high the previous week, data from Houston-based Baker Hughes showed on Friday. The gas-directed rig count dropped to 386 this week after climbing last week to its highest since March 22. It was the first gas rig count decline in three weeks. Recent rig count gains - the count has risen in eight of the last 13 weeks - have stirred industry talk that new investment in gas pipelines and processing plants, particularly in the East, are allowing producers to hook up more wells and pump even more supply into an already well-supplied market. Gas futures prices on Friday, which were down 2.7 cents at $3.693 per million British thermal units just before rig data was released at 1:02 p.m. EDT (1702 GMT), slipped about a penny after the report. The oil-focused rig count rose for the first time in three weeks, gaining eight to 1,369. The oil rig count hit a nine-month high of 1,413 in mid-June, Baker Hughes data showed. The oil count is down 33 rigs, or 2.4 percent, from the same week last year. Baker Hughes reported horizontal rigs, the type often used to extract oil or gas from shale, climbed for a third time in four weeks, picking up 15 rigs to 1,091. The horizontal count is down 8.5 percent from the record high of 1,193 set in May 2012. Despite recent natural gas rig gains, the count is down 59 percent since peaking in October 2011 at 936. But so far gas production has not slowed much, if at all, from the record high hit last year, boosted by the associated gas produced from more profitable shale oil and shale gas liquids wells. The U.S. Energy Information Administration still expects gas output in 2013 to hit a record high for a third straight year.