

A241951


Number of possible representations of n as a sum of distinct positive integers from the Fibonacci and Lucas sequences 0,1,1,2,3,5,8,13,... and 2,1,3,4,7,11,... (A000045 and A000032).


1



1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 8, 9, 10, 11, 12, 12, 15, 15, 16, 19, 19, 21, 22, 24, 26, 26, 28, 31, 31, 33, 35, 37, 40, 40, 44, 45, 46, 51, 51, 54, 57, 58, 61, 62, 65, 70, 69, 72, 76, 76, 81, 81, 86, 90, 89, 95, 97, 100, 105, 105, 110, 114, 114, 121, 121, 126, 133, 131, 138, 139, 142, 149, 147, 154, 160, 159, 165, 167
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OFFSET

0,4


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..20000
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.


EXAMPLE

a(10) = 6 because 10 can be represented in 6 possible ways as a sum of integers in the set {1,2,3,4,5,7,8,11,13,...}: 8+2, 7+3, 7+2+1, 5+4+1, 5+3+2, 4+3+2+1.


CROSSREFS

Cf. A000045, A000032, A000119.
Sequence in context: A112231 A213856 A173329 * A084630 A325393 A320388
Adjacent sequences: A241948 A241949 A241950 * A241952 A241953 A241954


KEYWORD

nonn


AUTHOR

Casey Mongoven, May 03 2014


EXTENSIONS

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


STATUS

approved



