AnimatedLoopCallback.js

animateWidth() {
    Animated.sequence([
      Animated.delay(3000),
      Animated.timing(this.state.width, {
        toValue: 400,
        duration: 2000
      })
    ]).start(() => {
      // Logic whenever an iteration finishes...
      this.animateWidth()
    });
}

componentDidMount() {
    this.animateWidth();
}