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, ....
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, 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, 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
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..19308
- J. Berstel, An Exercise on Fibonacci Representations, 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.
- D. A. Klarner, Representations of N as a sum of distinct elements from special sequences, part 1, part 2, Fib. Quart., 4 (1966), 289-306 and 322.
- Ron Knott, Ron Knott's Sequence Visualiser.
- Casey Mongoven, U(n) Rep Sequence no. 1; electronic music created with this sequence.
- Casey Mongoven, Sonification of multiple Fibonacci-related sequences, Annales Mathematicae et Informaticae, 41 (2013) pp. 175-192.
Programs
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Mathematica
imax = 10; f[1] = 1; f[2] = 4; f[n_] := f[n] = f[n-1] + f[n-2]; p = Product[1+x^f[i], {i, 1, imax}]; CoefficientList[p, x][[1;;f[imax]+1]] (* Jean-François Alcover, May 08 2019 *)
Extensions
a(0)=1 corrected by Alois P. Heinz, Sep 16 2015