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A103344 Number of representations of n as a sum of distinct elements of the Fibonacci-type sequence beginning 1, 4, 5, 9, 14, 23, 37, 60, ....

%I A103344 #18 Jan 05 2025 19:51:38
%S A103344 1,1,0,0,1,2,1,0,0,2,2,0,0,1,3,2,0,0,2,3,1,0,0,3,3,0,0,2,4,2,0,0,3,3,
%T A103344 0,0,1,4,3,0,0,3,5,2,0,0,4,4,0,0,2,5,3,0,0,3,4,1,0,0,4,4,0,0,3,6,3,0,
%U A103344 0,5,5,0,0,2,6,4,0,0,4,6,2,0,0,5,5,0,0,3,6,3,0,0,4,4,0,0,1,5,4,0,0
%N A103344 Number of representations of n as a sum of distinct elements of the Fibonacci-type sequence beginning 1, 4, 5, 9, 14, 23, 37, 60, ....
%H A103344 Alois P. Heinz, <a href="/A103344/b103344.txt">Table of n, a(n) for n = 0..19308</a>
%H A103344 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 A103344 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 A103344 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/seqvis.html">Ron Knott's Sequence Visualiser</a>.
%H A103344 Casey Mongoven, <a href="http://caseymongoven.com/catalogue/b153.html">U(n) Rep Sequence no. 1</a>; electronic music created with this sequence.
%H A103344 Casey Mongoven, <a href="http://ami.ektf.hu/uploads/papers/finalpdf/AMI_41_from175to192.pdf">Sonification of multiple Fibonacci-related sequences</a>, Annales Mathematicae et Informaticae, 41 (2013) pp. 175-192.
%t A103344 imax = 10;
%t A103344 f[1] = 1; f[2] = 4; f[n_] := f[n] = f[n-1] + f[n-2];
%t A103344 p = Product[1+x^f[i], {i, 1, imax}];
%t A103344 CoefficientList[p, x][[1;;f[imax]+1]] (* _Jean-François Alcover_, May 08 2019 *)
%Y A103344 Cf. A000121, A000119, A067595, A003263, A103343.
%K A103344 nonn
%O A103344 0,6
%A A103344 _Casey Mongoven_, Feb 01 2005
%E A103344 a(0)=1 corrected by _Alois P. Heinz_, Sep 16 2015