

A103344


Number of representations of n as a sum of distinct elements of the Fibonaccitype 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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,6


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. 491498, 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), 289306 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 Fibonaccirelated sequences, Annales Mathematicae et Informaticae, 41 (2013) pp. 175192.


MATHEMATICA

imax = 10;
f[1] = 1; f[2] = 4; f[n_] := f[n] = f[n1] + f[n2];
p = Product[1+x^f[i], {i, 1, imax}];
CoefficientList[p, x][[1;; f[imax]+1]] (* JeanFrançois Alcover, May 08 2019 *)


CROSSREFS

Cf. A000121, A000119, A067595, A003263, A103343.
Sequence in context: A303708 A319138 A281081 * A123484 A008626 A058626
Adjacent sequences: A103341 A103342 A103343 * A103345 A103346 A103347


KEYWORD

nonn


AUTHOR

Casey Mongoven, Feb 01 2005


EXTENSIONS

a(0)=1 corrected by Alois P. Heinz, Sep 16 2015


STATUS

approved



