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%I #11 Sep 16 2015 11:31:17
%S 1,1,1,2,2,3,4,4,5,6,7,8,8,10,11,12,14,14,16,18,18,21,22,23,26,26,29,
%T 31,32,35,36,39,41,41,46,47,49,53,52,57,60,60,65,66,70,74,73,79,81,84,
%U 89,88,94,97,97,105,105,109,115,113,121,124,125,132,132,139,143,141,151,152,157,164,161,171,175
%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 0,2,2,4,6,10,16,... (A000045 and A118658).
%H Alois P. Heinz, <a href="/A241948/b241948.txt">Table of n, a(n) for n = 0..17711</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) = 7 because 10 can be represented in 7 possible ways as a sum of integers in the set {1,2,3,4,5,6,8,10,13,16,...}: 10, 8+2, 6+4, 6+3+1, 5+4+1, 5+3+2, 4+3+2+1.
%Y Cf. A118658, 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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