Ekhad, Shalosh B.; Zeilberger, Doron Automatic counting of tilings of skinny plane regions. (English) Zbl 1302.05032 Blackburn, Simon R. (ed.) et al., Surveys in combinatorics 2013. Papers based on the 24th British combinatorial conference, London, UK, June 30 – July 5, 2013. Cambridge: Cambridge University Press (ISBN 978-1-107-65195-1/pbk; 978-1-139-50674-8/ebook). London Mathematical Society Lecture Note Series 409, 363-378 (2013). The paper deals with counting the number of tilings of some plane regions. The authors were inspired by a problem proposed by D. Knuth. The results are proved by an inductive method using \(C\)-finite sequences.The article is accompanied with Maple packages. In particular, they count the number of domino tilings of a rectangle, of a holey rectangle, of a cross.For the entire collection see [Zbl 1286.05002]. Reviewer: Elizaveta Zamorzaeva (Chişinău) Cited in 2 Documents MSC: 05B45 Combinatorial aspects of tessellation and tiling problems 05A15 Exact enumeration problems, generating functions Keywords:tilings; counting; plane regions; Maple packages; \(C\)-finite sequences; domino tilings; holey rectangle; cross Software:RITSUF; TILINGS; Maple PDFBibTeX XMLCite \textit{S. B. Ekhad} and \textit{D. Zeilberger}, Lond. Math. Soc. Lect. Note Ser. 409, 363--378 (2013; Zbl 1302.05032) Full Text: DOI arXiv Online Encyclopedia of Integer Sequences: Golden rectangle numbers: F(n)*F(n+1), where F(n) = A000045(n) (Fibonacci numbers). a(n) = F(n)^2 + F(n+1)^2 + F(n+2)^2, where F(n) denotes the n-th Fibonacci number. Number of domino tilings of a cross whose center is a 4 X 4 square and in which each of the four arms has length n.