Geodesic
A Note on Combinations
Canadian mathematical bulletin, Tome 9 (1966) no. 5, pp. 675-677

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We call k integers x1 < x2 ... < xk chosen from 1, 2, ..., n} a k-choice (combination) from n. With 1, 2, ..., n arranged in a circle, so that 1 and n are consecutive, we have a circular k-choice from n. A part of a k-choice from n is a sequence of consecutive integers not contained in a longer one. Let denote the number of circular k-choices from n with exactly r parts all ≤ w. 
Abramson, M.; Moser, W. A Note on Combinations. Canadian mathematical bulletin, Tome 9 (1966) no. 5, pp. 675-677. doi: 10.4153/CMB-1966-082-5
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     doi = {10.4153/CMB-1966-082-5},
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