Number of compositions of n into Fibonacci numbers considering also the extension.

[Davide Rotondo]

Hi to all dear seqfans. What I proposed to you today is an old interest for me. I didn't find anything matching in OEIS with this sequence so I hope you will find it interesting.

Fibonacci sequence and the extension

…,-21,13,-8,5,-3,2,-1,1,0,1,1,2,3,5,8,13,21,...

how many times does the value appear

…

-21=1

-8=1

-3=1

-1=1

0=1

1=3

2=2

3=1

5=2

8=1

13=2

21=1

…

right to left: a(n) = a(n-1)*3 + a(n-2)*2 + a(n-3) + a(n-5)*2 + a(n-8) + a(n-13)*2 + a(n-21)+ …

and left to right:

a(n) = a(n+1) + a(n+3) + a(n+8) + a(n+21) + … 

i don’t know but in this case a(n +/- 0) i considered that the value must be multiplied by 2

the sequence

1,8,54,468,3150,...

All the best

Davide