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We present the results of a diffusion Monte Carlo calculation on the groundstate energy of 4He adsorbed in the interstitial channels of a bundle of (10, 10) nanotubes. The one-dimensionality of that system is analyzed by comparing the bundle results with the equation of state of purely 1D 4He. In spite of the narrowness of the intersites, significant differences in both the binding energy and the equilibrium density of the two systems appear. Moreover, additional attraction provided by neighboring interchannels filled with helium modifies in a sizeable amount the equation of state of a single intersite.