Search: id:A092921
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%I A092921
%S A092921 0,1,0,1,1,0,1,1,1,0,1,2,1,1,0,1,3,2,1,1,0,1,5,4,2,1,1,0,1,8,7,4,2,1,1,
%T A092921 0,1,13,13,8,4,2,1,1,0,1,21,24,15,8,4,2,1,1,0,1,34,44,29,16,8,4,2,1,1,
               0,
%U A092921 1,55,81,56,31,16,8,4,2,1,1,0,1,89,149,108,61,32,16,8,4,2,1
%N A092921 Array F(k,n) read by antidiagonals: k-generalized Fibonacci numbers.
%C A092921 For all k>=1, the k-generalized Fibonacci number F(k,n) satisfies the 
               recurrence obtained by adding more terms to the recurrence of the 
               Fibonacci numbers.
%C A092921 The number of tilings of an 1 X n rectangle with tiles of size 1 X 1, 
               1 X 2, ..., 1 X k is F(k,n).
%C A092921 T(k,n) is the number of 0-balanced ordered trees with n edges and height 
               k (height is the number of edges from root to a leaf). - Emeric Deutsch 
               (deutsch(AT)duke.poly.edu), Jan 19 2007
%D A092921 Nathaniel D. Emerson, A Family of Meta-Fibonacci Sequences Defined by 
               Variable-Order Recursions, Journal of Integer Sequences, Vol. 9 (2006), 
               Article 06.1.8.
%D A092921 I. Flores, k-Generalized Fibonacci numbers, Fib. Quart., 5 (1967), 258-266.
%D A092921 H. Gabai, Generalized Fibonacci k-sequences, Fib. Quart., 8 (1970), 31-38.
%D A092921 R. Kemp, Balanced ordered trees, Random Structures and Alg., 5 (1994), 
               pp. 99-121.
%D A092921 E. P. Miles jr., Generalized Fibonacci numbers and associated matrices, 
               The Amer. Math. Monthly, 67 (1960) 745-752.
%D A092921 M. D. Miller, On generalized Fibonacci numbers, The Amer. Math. Monthly, 
               78 (1971) 1108-1109.
%H A092921 E. S. Egge, <a href="http://www.arXiv.org/abs/math.CO/0109219">Restricted 
               permutations related to Fibonacci numbers...</a>.
%H A092921 E. S. Egge, <a href="http://arXiv.org/abs/math.CO/0307050">Restricted 
               3412-Avoiding Involutions</a>
%H A092921 E. S. Egge and T. Mansour, <a href="http://arXiv.org/abs/math.CO/0203226">
               Restricted permutations, Fibonacci numbers and k-generalized Fibonacci 
               numbers</a>.
%H A092921 E. S. Egge and T. Mansour, <a href="http://arXiv.org/abs/math.CO/0209255">
               231-avoiding involutioms and Fibonacci numbers</a>.
%H A092921 A. Flaxman, A. W. Harrow and G. B. Sorkin, <a href="http://www.combinatorics.org/
               Volume_11/Abstracts/v11i1r8.html">Strings with maximally many distinct 
               subsequences and substrings</a>
%F A092921 F(k, n)=F(k, n-1)+F(k, n-2)+...+F(k, n-k); F(k, 1)=1 and for n<=0, F(k, 
               n)=0.
%F A092921 G.f.: x/[1-sum(i=0..k, x^i)].
%o A092921 (PARI) F(k,n)=if(n<2,if(n<1,0,1),sum(i=1,k,F(k,n-i)))
%Y A092921 Columns converge to 2^(n-2).
%Y A092921 Rows 1-8 are (shifted) A057427, A000045, A000073, A000078, A001591, A001592, 
               A066178, A079262.
%Y A092921 Essentially a reflected version of A048887. See A048004 and A126198 for 
               closely related arrays.
%Y A092921 Sequence in context: A105806 A129501 A158511 this_sequence A029387 A070878 
               A060959
%Y A092921 Adjacent sequences: A092918 A092919 A092920 this_sequence A092922 A092923 
               A092924
%K A092921 nonn,tabl
%O A092921 0,12
%A A092921 Ralf Stephan, Apr 17 2004

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