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A298343
a(n) = a(n-1) + a(n-2) + a([2n/3]), where a(0) = 1, a(1) = 2, a(2) = 3.
2
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
0,2
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
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 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 09 2018
STATUS
approved