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Zuwen Luo and Kexiang Xu, <a href="https://doi.org/10.1016/j.amc.2024.128883">The number of connected sets in Apollonian networks</a>, Applied Mathematics and Computation, Volume 479, 2024. On <a href="https://www.researchgate.net/publication/381160571_The_number_of_connected_sets_in_Apollonian_networks
0, 1, 3, 7, 15, 30, 58, 110, 206, 383, 709, 1309, 2413, 4444, 8180, 15052, 27692, 50941, 93703, 172355, 317019, 583098, 1072494, 1972634, 3628250, 6673403, 12274313, 22575993, 41523737, 76374072, 140473832, 258371672, 475219608, 874065145, 1607656459, 2956941247
<a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3, -2, 0, -1, 1).
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L. Moset and E. L. Whitney, Weighted compositions, Canad. Math. Bull. 4 (1961) 39-43.
L. Moser and E. L. Whitney, <a href="https://doi.org/10.4153/CMB-1961-006-0">Weighted compositions</a>, Canad. Math. Bull. 4 (1961), 39-43.
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