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

0,3

Comments

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

Links

Table of n, a(n) for n=0..34.

Formula

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

Prog

(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

Crossrefs

Cf. A000032, A000045, A116470.

Cf. A076739, A288039.

Sequence in context: A001591 A194628 A003240 * A280543 A282566 A251706

Adjacent sequences: A378695 A378696 A378697 * A378699 A378700 A378701

Keyword

nonn

Author

Davide Rotondo, Dec 04 2024

Status

approved