A121550 Number of ordered ways of writing n as a sum of three Fibonacci numbers (only one 1 is considered as a Fibonacci number).
0, 0, 1, 3, 6, 7, 9, 9, 10, 9, 12, 12, 9, 9, 10, 12, 12, 12, 12, 6, 9, 6, 12, 13, 9, 12, 12, 9, 12, 6, 12, 6, 0, 9, 6, 9, 15, 9, 13, 9, 6, 12, 9, 12, 9, 0, 12, 6, 6, 12, 0, 6, 0, 0, 9, 6, 9, 12, 9, 15, 9, 6, 13, 6, 9, 6, 0, 12, 9, 9, 12, 0, 9, 0, 0, 12, 6, 6, 6, 0, 12, 0, 0, 6, 0, 0, 0, 0, 9, 6, 9, 12
Offset: 1
Keywords
Examples
a(6)=7 because we have 6=1+2+3=1+3+2=2+1+3=2+3+1=3+1+2=3+2+1=2+2+2.
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..10000
Programs
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Maple
with(combinat): g:=sum(z^fibonacci(i),i=2..30)^3: gser:=series(g,z=0,130): seq(coeff(gser,z,n),n=1..126);
Formula
G.f.: (Sum_{i>=2} x^Fibonacci(i))^3.
a(n) = A121548(n,3).