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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 (list; graph; refs; listen; history; text; internal format)
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

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

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

Cf. A001622, A000045, A298338.

Sequence in context: A128305 A328881 A298349 * A201361 A129700 A197466

Adjacent sequences:  A298340 A298341 A298342 * A298344 A298345 A298346

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 09 2018

STATUS

approved

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Last modified January 19 21:47 EST 2020. Contains 331066 sequences. (Running on oeis4.)