Amazon said that it had “nearly tripled” the number of customers for its Appstore in the last three months of 2011 compared to the prior sequential quarter, although it did not provide numbers to support this.

The company also said that its customer base had downloaded more apps from its store during the fourth quarter than all previous quarters combined – again without putting a figure on this.

Amazon’s app store is currently available to customers in the US, where its position has been bolstered by the launch of the company’s Kindle Fire Android-powered tablet.

According to a recent survey from Flurry, Kindle Fire users have grown to represent 36 percent of Android tablet app sessions, slightly ahead of Samsung’s more established Galaxy Tab line. Kindle Fire users have also shown an appetite for paid-for apps, making the Appstore a lucrative alternative to Android Market.