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%I #9 Sep 16 2015 11:34:41
%S 1,1,1,2,1,2,3,2,4,5,4,6,5,5,8,8,9,10,10,10,11,12,13,15,18,16,17,19,
%T 17,22,24,22,26,26,24,29,28,30,34,35,35,35,38,38,41,46,43,46,52,46,52,
%U 54,51,59,60,58,63,63,64,67,68,71,71,80,78,76,85,80,84,96,87,94,102,93,102,102,101,111,114,115,115,117,121,119,129
%N Number of possible representations of n as a sum of distinct positive integers from the Fibonacci-type sequences 0,1,1,2,3,5,8,13,... and 0,3,3,6,9,15,... (A000045 and A022086).
%H Alois P. Heinz, <a href="/A241949/b241949.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) = 4 because 10 can be represented in 4 possible ways as a sum of integers in the set {1,2,3,5,6,8,9,13,15,...}: 9+1, 8+2, 6+3+1, 5+3+2.
%Y Cf. A022086, A000045, 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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