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

0,6

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. 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.

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

Cf. A000121, A000119, A067595, A003263, A103343.

Sequence in context: A349396 A330462 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