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 A298340 a(n) = a(n-1) + a(n-2) + a([n/3]), where a(0) = 1, a(1) = 1, a(2) = 1. 2
 1, 1, 1, 3, 5, 9, 15, 25, 41, 69, 113, 185, 303, 493, 801, 1303, 2113, 3425, 5553, 8993, 14561, 23579, 38165, 61769, 99975, 161785, 261801, 423655, 685525, 1109249, 1794887, 2904249, 4699249, 7603683, 12303117, 19906985, 32210405, 52117693, 84328401 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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..999 MATHEMATICA a[0] = 1; a[1] = 1; a[2] = 1; a[n_] := a[n] = a[n - 1] + a[n - 2] + a[Floor[n/3]]; Table[a[n], {n, 0, 30}]  (* A298340 *) CROSSREFS Cf. A001622, A000045, A298338. Sequence in context: A128587 A001595 A092369 * A061969 A034084 A018342 Adjacent sequences:  A298337 A298338 A298339 * A298341 A298342 A298343 KEYWORD nonn,easy AUTHOR Clark Kimberling, Feb 09 2018 STATUS approved

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Last modified December 9 08:20 EST 2019. Contains 329877 sequences. (Running on oeis4.)