A378698 Number of compositions of n into parts whose sizes are Fibonacci or Lucas numbers.

1, 1, 2, 4, 8, 16, 31, 62, 123, 243, 481, 953, 1887, 3737, 7399, 14652, 29014, 57452, 113767, 225279, 446095, 883352, 1749201, 3463746, 6858864, 13581833, 26894570, 53256275, 105457382, 208825335, 413513204, 818833458, 1621443338, 3210760963, 6357907009

Offset: 0

Author

Davide Rotondo, Dec 04 2024

Keywords

• nonn

Comments

a(n+1)/a(n) approximate the constant r = 1.9801869...

Crossrefs

Cf. A000032, A000045, A116470.

Cf. A076739, A288039.

Programs

PARI

A116470(n) = if(n<6, n, if(n%2, fibonacci(n\2+3), fibonacci(n\2)+fibonacci(n\2+2)))
a(max_n) = {Vec(1/(1+sum(k=1,max_n-1, -1*x^A116470(k)))+O(x^max_n)); } \\ Thomas Scheuerle, Dec 04 2024

Formula

G.f.: 1/(1 - Sum_{k>=1} x^A116470(k)). - Thomas Scheuerle, Dec 04 2024