A298343 a(n) = a(n-1) + a(n-2) + a([2n/3]), where a(0) = 1, a(1) = 2, a(2) = 3.

1, 2, 3, 8, 14, 30, 58, 102, 190, 350, 598, 1050, 1838, 3078, 5266, 8942, 14806, 24798, 41442, 68078, 112598, 185942, 303806, 498690, 817302, 1330798, 2172898, 3545138, 5759478, 9372694, 15244770, 24730062, 40160774, 65194642, 105659222, 171352554, 277829078

Offset: 0

Author

Clark Kimberling, Feb 09 2018

Keywords

• nonn
• easy

Comments

a(n)/a(n-1) -> (1 + sqrt(5))/2, the golden ratio (A001622), so that (a(n)) has the growth rate of the Fibonacci numbers (A000045). See A298338 for a guide to related sequences.

Links

• Clark Kimberling, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A001622, A000045, A298338.

Programs

Maple

A298343 := proc(n)
    option remember ;
    if n <=2 then
        n+1 ;
    else
        procname(n-1)+procname(n-2)+procname(floor(2*n/3)) ;
    end if;
end proc:
seq(A298343(n),n=0..80) ; # R. J. Mathar, Apr 26 2022

Mathematica

a[0] = 1; a[1] = 2; a[2] = 3;
a[n_] := a[n] = a[n - 1] + a[n - 2] + a[Floor[2n/3]];
Table[a[n], {n, 0, 30}]  (* A298343 *)