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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, ....
21
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
0,6
LINKS
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.
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.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Casey Mongoven, Feb 01 2005
EXTENSIONS
a(0)=1 corrected by Alois P. Heinz, Sep 16 2015
STATUS
approved