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%I #13 Jan 05 2025 19:51:38
%S 1,1,0,1,2,2,1,1,2,3,2,0,2,3,3,2,1,3,4,3,1,2,3,4,3,0,3,5,4,2,2,4,5,3,
%T 0,3,4,4,3,1,4,6,5,2,3,5,6,4,0,4,6,5,3,2,5,6,4,1,3,4,5,4,0,4,7,6,3,3,
%U 6,8,5,0,5,7,6,4,2,6,8,6,2,4,6,7,5,0,5,8,6,3,3,6,7,4,0,4,5,5,4,1,5
%N Number of representations of n as a sum of distinct elements of the Fibonacci-type sequence beginning 3, 1, 4, 5, 9, 14, 23, 37, ....
%H Alois P. Heinz, <a href="/A103343/b103343.txt">Table of n, a(n) for n = 0..11933</a>
%H J. Berstel, <a href="http://www-igm.univ-mlv.fr/~berstel/Articles/2001ExerciceAldo.pdf">An Exercise on Fibonacci Representations</a>, RAIRO/Informatique Theorique, Vol. 35, No 6, 2001, pp. 491-498, in the issue dedicated to Aldo De Luca on the occasion of his 60th anniversary.
%H D. A. Klarner, Representations of N as a sum of distinct elements from special sequences, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/4-4/klarner-a.pdf">part 1</a>, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/4-4/klarner-b.pdf">part 2</a>, Fib. Quart., 4 (1966), 289-306 and 322.
%H Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/seqvis.html">Ron Knott's Sequence Visualiser</a>.
%H Casey Mongoven, <a href="http://caseymongoven.com/catalogue/b152.html">V(n) Rep Sequence no. 1</a>; electronic music created with this sequence.
%Y Cf. A000121, A000119, A067595, A003263, A103344.
%K nonn
%O 0,5
%A _Casey Mongoven_, Feb 01 2005
%E a(0)=1 corrected by _Alois P. Heinz_, Sep 16 2015