A121551 Number of parts in all the compositions of n into Fibonacci numbers (i.e., in all ordered sequences of Fibonacci numbers having sum n; only one 1 is considered as a Fibonacci number).
1, 3, 8, 19, 44, 98, 213, 457, 965, 2018, 4183, 8604, 17594, 35780, 72428, 146024, 293335, 587386, 1172836, 2335761, 4640947, 9201531, 18208325, 35967145, 70929855, 139667107, 274630886, 539309530, 1057789244, 2072370716, 4055782140, 7929563974, 15488792843
Offset: 1
Keywords
Examples
a(4)=19 because the compositions of 8 into Fibonacci numbers are [1,3],[2,2],[3,1],[1,1,2],[1,2,1],[2,1,1] and [1,1,1,1], having a total of 2+2+2+3+3+3+4 = 19 parts.
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..2000
Programs
-
Maple
with(combinat): g:=sum(z^fibonacci(i),i=2..20)/(1-sum(z^fibonacci(i),i=2..20))^2: gser:=series(g,z=0,48): seq(coeff(gser,z,n),n=1..35);
Formula
G.f.: (Sum_{i>=2} z^Fibonacci(i))/(1 - Sum_{i>=2} z^Fibonacci(i))^2.
Comments