* Gas rig count sheds 16, first drop in three weeks * Horizontal rigs gain for first time in three weeks * Oil rig count jumps 19 to 1,376 NEW YORK, Nov 1 (Reuters) - The number of rigs drilling for natural gas in the United States fell this week for the first time in three weeks, dropping by 16 to 360, data from Houston-based Baker Hughes showed on Friday. The gas-directed rig count, which hit a six-month high of 401 seven weeks ago, has increased in 11 of the last 19 weeks and is still above the 18-year low of 349, set in late June. A rising gas rig count can stir talk that new pipelines and processing plants, particularly in the East, may be encouraging producers to hook up more wells and pump more supply into an already well-supplied market. Gas futures prices on Friday, which were down about 5 cents at $3.532 per million British thermal units just before the rig data was released at 1:02 p.m. EDT (1702 GMT), were still trading at about that level at 1:15 p.m. The oil-focused rig count rose for the first time in four weeks, climbing 19 to 1,376. The oil rig count hit a nine-month high of 1,413 in mid-June, Baker Hughes data showed. The oil count is down just 3 rigs from the same week last year. Baker Hughes reported that horizontal rigs, the type often used to extract oil or gas from shale, saw their first gain in three weeks, adding six to 1,104. The horizontal count is down 7.5 percent from the record high of 1,193 in May 2012. While the gas rig count is off 62 percent since peaking in October 2011 at 936, gas production has not showed any signs of slowing. The associated gas produced from more profitable shale oil and shale gas liquids wells has kept dry gas flowing at or near a record pace. U.S. Energy Information Administration data on Thursday showed that gross gas production hit a record high in August, climbing to 74.82 billion cubic feet per day. Output in August was running about 2.3 bcfd, or 3.1 percent, above the same month last year. The EIA still expects U.S. gas production in 2013 to hit a record high for the third straight year.