An exact formula, valid for any number of links and any constant angle between links, is derived for the mean square end-end length of a chain, subject to the following conditions. Any three successive bonds must be in a trans configuration or one of two gauche configurations. The energy of a trans configuration is lower by E (per mole) than the energy of a gauche configuration. The excluded volume problem is ignored.
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Richard P. Smith (1960) studied this question.