Generalized Jacobsthal numbers and restricted k-ary words

[1] G. E. Andrews, The Theory of Partitions, Cambridge University Press, 1998.Search in Google Scholar

[2] 1987 Austrian Olympiad, Crux Mathematicorum, 15 (1989) 264.Search in Google Scholar

[3] A. T. Benjamin and J. J. Quinn, Proofs that Really Count: The Art of Combinatorial Proof, Mathematical Association of America, Washington, DC, 2003.10.5948/9781614442080Search in Google Scholar

[4] V. Bruyére, Automata and numeration systems, S´em. Lothar. Combin., 35 (1995) Art. B35b.Search in Google Scholar

[5] R. De Castro, A. Ram´ırez and J. L. Ram&ıacute;rez, Applications in enumerative combinatorics of infinite weighted automata and graphs, Sci. Ann. Comput. Sci., 24 (2014) 137–171.Search in Google Scholar

[6] J. Y. Choi, A generalization of Collatz functions and Jacobsthal numbers, J. Integer Seq., 21 (2018) Art. 18.5.4.Search in Google Scholar

[7] M. Delest, Algebraic languages: a bridge between combinatorics and computer science, DI-MACS Ser. Discrete Math. Theoret. Comput. Sci., 24 (1996) 71–88.Search in Google Scholar

[8] P. Flajolet and R. Sedgewick, Analytic Combinatorics, Cambridge University Press, 2009.10.1017/CBO9780511801655Search in Google Scholar

[9] R. Honsberger, From Erd˝os to Kiev: Problems of Olympiad Caliber, Mathematical Association of America, Washington, DC, 1996.Search in Google Scholar

[10] T. Koshy and R. P. Grimaldi, Ternary words and Jacobsthal numbers, Fibonacci Quart., 55 (2017) 129–136.Search in Google Scholar

[11] H. Prodinger, Ternary Smirnov words and generating functions, Integers, 18 (2018) #A69.Search in Google Scholar

[12] J. Sakarovitch, Elements of Automata Theory, Cambridge University Press, 2009.10.1017/CBO9781139195218Search in Google Scholar

[13] M. A. Shattuck and C. G. Wagner, Parity theorems for statistics on lattice paths and Laguerre configurations, J. Integer Seq., 8 (2005) Art. 5.5.1.10.37236/1977Search in Google Scholar

[14] M. A. Shattuck and C. G. Wagner, A new statistic on linear and circular r-mino arrangements, Electron. J. Combin., 13 (2006) #R42.10.37236/1068Search in Google Scholar

[15] N. J. Sloane, On-Line Encyclopedia of Integer Sequences, available at http://oeis.org.Search in Google Scholar