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A298340
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a(n) = a(n-1) + a(n-2) + a([n/3]), where a(0) = 1, a(1) = 1, a(2) = 1.
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2
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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
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OFFSET
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0,4
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COMMENTS
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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.
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LINKS
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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