Frosini, A.; Rinaldi, S. On the sequence A079500 and its combinatorial interpretations. (English) Zbl 1103.05006 J. Integer Seq. 9, No. 3, Article 06.3.1, 13 p. (2006). Summary: We present some combinatorial structures enumerated by the sequence A079500 in Sloane’s On-Line Encyclopedia of Integer Sequences and determine simple bijections among these structures. Then we investigate the nature of the generating function of the sequence, and prove that it is not differentiably finite. Cited in 1 Document MSC: 05A15 Exact enumeration problems, generating functions 05B45 Combinatorial aspects of tessellation and tiling problems 05B50 Polyominoes Keywords:combinatorial structures; generating function Software:OEIS PDFBibTeX XMLCite \textit{A. Frosini} and \textit{S. Rinaldi}, J. Integer Seq. 9, No. 3, Article 06.3.1, 13 p. (2006; Zbl 1103.05006) Full Text: EuDML EMIS Online Encyclopedia of Integer Sequences: a(n) = (4^n - 1)/3. Number of balanced ordered trees with n nodes. a(n) = Sum_{m=1..n} T(m,n+1-m), array T as in A048887. Negabinary numbral addition table read by antidiagonals. Irreducible elements in OR-numbral arithmetic. Number of integers i=1,2,...,n such that (n,i) has Property F3*, i.e., i and n are consecutive terms of a sequence b(k) satisfying b(1)=1, b(n) = (b(n-1) OR 2*b(n-1)) + b(n-2), where the OR is taken bitwise. Squares in OR-numbral arithmetic. Number of divisors of n in OR-numbral arithmetic. Number of compositions of the integer n in which the first part is >= the other parts.