In pulsed optically detected magnetic resonance (ODMR) spectroscopy, a lock-in amplifier is used to monitor the signal which is phase-matched to the duty cycle of an applied sequence of pulses. However, since the desired signals reside atop a much larger amplitude-modulated signal, lock-in amplification methods are difficult to use. Commerically available photon counters are of limited use, because the pulsed ODMR method requires sequential counting over several time intervals, often with minimum time delay between the intervals. The multiaccumulator photon counter described here is capable of such sequential counting over as many as four intervals. The microprocessor which controls the counter algebraically manipulates the photon counts during each of the duty cycles. The result is an inexpensive yet versatile photon counter which is suited for pulsed ODMR and other applications in which sequential counting is necessary.