This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A218396 #11 Nov 09 2012 20:37:40 %S A218396 1,1,1,3,2,3,8,2,9,8,8,32,6,9,32,8,38,30,32,150,6,33,32,32,158,30,38, %T A218396 174,30,176,150,150,870,24,33,152,32,182,150,158,894,30,182,174,174, %U A218396 1014,144,176,990,150,1014,864,870,5904,24,153,152,152,902,150,182,1014,150,1022,894,894,6054,144 %N A218396 Number of compositions of n into distinct (nonzero) Fibonacci numbers. %H A218396 Joerg Arndt and Alois P. Heinz, <a href="/A218396/b218396.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..200 from Joerg Arndt) %e A218396 There are a(37)=182 such compositions of 37. Each of the 6 partitions of 37 into distinct Fibonacci numbers corresponds to m! compositions (where m is the number of parts): %e A218396 #: partition ( m! compositions) %e A218396 1: 1 2 5 8 21 (120 compositions) %e A218396 2: 1 2 13 21 ( 24 compositions) %e A218396 3: 1 2 34 ( 6 compositions) %e A218396 4: 3 5 8 21 ( 24 compositions) %e A218396 5: 3 13 21 ( 6 compositions) %e A218396 6: 3 34 ( 2 compositions) %e A218396 The number of compositions is 120 + 24 + 6 + 24 + 6 + 2 = 182. %Y A218396 Cf. A032021 (compositions into distinct odd numbers). %Y A218396 Cf. A000119 (partitions into distinct nonzero Fibonacci numbers), A000700 (partitions into distinct odd numbers). %Y A218396 Cf. A076739 (compositions into Fibonacci numbers). %K A218396 nonn %O A218396 0,4 %A A218396 _Joerg Arndt_, Oct 28 2012