In this paper, the problem of sequential waveform design for target enumeration for cognitive multiple-input single-output (MISO) radar is investigated. In the proposed technique, the transmit spatial waveform is adaptively determined at each step based on observations in the previous steps. The waveform is determined to minimize an approximated lower bound on the average sample number (ASN) required to achieve given error rates. The algorithm is tested via simulations and shown to exhibit superior performance compared to orthogonal waveform transmission.