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In this paper, we investigate the resource allocation design for integrated sensing and communication (ISAC) in distributed antenna networks (DANs). In particular, coordinated by a central processor (CP), a set of remote radio heads (RRHs) provide communication services to multiple users and sense several target locations within an ISAC frame. To avoid the severe interference between the information transmission and the radar echo, we propose to divide the ISAC frame into a communication phase and a sensing phase. During the communication phase, the data signal is generated at the CP and then conveyed to the RRHs via fronthaul links. As for the sensing phase, based on pre-determined RRH-target pairings, each RRH senses a dedicated target location with a synthesized highly-directional beam and then transfers the samples of the received echo to the CP via its fronthaul link for further processing of the sensing information. Taking into account the limited fronthaul capacity and the quality-of-service requirements of both communication and sensing, we jointly optimize the durations of the two phases, the information beamforming, and the covariance matrix of the sensing signal for minimization of the total energy consumption over a given finite time horizon. To solve the formulated non-convex design problem, we develop a low-complexity alternating optimization algorithm which converges to a suboptimal solution. Simulation results show that the proposed scheme achieves significant energy savings compared to two baseline schemes. Moreover, our results reveal that for efficient ISAC in wireless networks, energy-focused short-duration pulses are favorable for sensing while low-power long-duration signals are preferable for communication.