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For n>=0: a(n+2) is the number of length-n strings words with letters {0,1,2,3} where the letter x is followed by at least x zeros, see Fxtbook link. [Joerg Arndt, Apr 08 2011]
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Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992.
Álvaro Serrano Holgado and Luis Manuel Navas Vicente, <a href="https://arxiv.org/abs/2301.11747">The zeta function of a recurrence sequence of arbitrary degree</a>, arXiv:2301.11747 [math.NT], 2023.
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Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, <a href="https://arxiv.org/ftp/arxiv/papers/0911abs/0911.4975.pdf">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992.
Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articlesA000051/FonctionsGeneratricesa000051_2.pdf">1031 Generating Functions and Conjectures</a>, Université du Québec à Montréal, Appendix to Thesis, Montreal, 1992.
Simon Plouffe, <a href="httphttps://www.lacim.uqamarxiv.caorg/ftp/arxiv%7Eplouffepapers/articles0911/MasterThesis0911.4975.pdf">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992.
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