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 A298341 a(n) = a(n-1) + a(n-2) + a([n/3]), where a(0) = 1, a(1) = 2, a(2) = 3. 2
 1, 2, 3, 7, 12, 21, 36, 60, 99, 166, 272, 445, 729, 1186, 1927, 3134, 5082, 8237, 13355, 21628, 35019, 56707, 91786, 148553, 240438, 389090, 629627, 1018883, 1648676, 2667725, 4316673, 6984670, 11301615, 18286730, 29588790, 47875965, 77465484, 125342178 (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[n/3]]; Table[a[n], {n, 0, 30}]  (* A298341 *) CROSSREFS Cf. A001622, A000045, A298338. Sequence in context: A056179 A222196 A184696 * A027675 A298353 A054176 Adjacent sequences:  A298338 A298339 A298340 * A298342 A298343 A298344 KEYWORD nonn,easy AUTHOR Clark Kimberling, Feb 09 2018 STATUS approved

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Last modified January 27 17:58 EST 2020. Contains 331296 sequences. (Running on oeis4.)