This study investigated students' physics motivational beliefs including their physics self-efficacy, interest, perceived recognition, and identity in a traditionally taught two-semester college calculus-based introductory physics sequence (referred to as physics 1 and physics 2). We studied whether and how these motivational beliefs evolve in this course sequence in terms of the average scores and the predictive relationships among them. The results show that both female and male students' physics self-efficacy and interest decreased from physics 1 to physics 2, while there was no statistically significant change in students' perceived recognition and identity. We found signatures of an inequitable and noninclusive learning environment in that not only was there a gender difference in students' motivational beliefs disadvantaging women, but the gender difference in perceived recognition increased from physics 1 to physics 2. We used structural equation modeling (SEM) to investigate the predictive relationships among students' motivational beliefs in physics 1 and physics 2. Analysis revealed that perceived recognition from others, e.g., instructors and teaching assistants, was the largest predictor of physics identity in both courses, and the role played by perceived recognition was even more important in physics 2 for predicting identity and mediating the gender difference in self-efficacy. Our findings suggest that perceived recognition is very important for the development of students' physics identity in both physics 1 and 2. However, female students feel less recognized in the current learning environment and this gender difference grows from physics 1 to physics 2. Instructors should be trained to create an equitable and inclusive learning environment, in which all students feel recognized and supported appropriately and develop a stronger physics self-efficacy, interest, and identity.