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

0,4

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), 289-306 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: A213856 A173329 A369113 * 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