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, 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
Offset: 0
Keywords
Examples
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.
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), 289-306 and 322.
Extensions
a(0)=1 from Alois P. Heinz, Sep 16 2015