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%I #9 Sep 16 2015 11:37:15
%S 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,
%T 26,28,31,31,33,35,37,40,40,44,45,46,51,51,54,57,58,61,62,65,70,69,72,
%U 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
%N 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).
%H Alois P. Heinz, <a href="/A241951/b241951.txt">Table of n, a(n) for n = 0..20000</a>
%H D. A. Klarner, Representations of N as a sum of distinct elements from special sequences, <a href="http://www.fq.math.ca/Scanned/4-4/klarner-a.pdf">part 1</a>, <a href="http://www.fq.math.ca/Scanned/4-4/klarner-b.pdf">part 2</a>, Fib. Quart., 4 (1966), 289-306 and 322.
%e 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.
%Y Cf. A000045, A000032, A000119.
%K nonn
%O 0,4
%A _Casey Mongoven_, May 03 2014
%E a(0)=1 from _Alois P. Heinz_, Sep 16 2015
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