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A274058
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Relative of Hofstadter Q-sequence: a(n) = max(0, n+32478) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0.
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9
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6, 32479, 32480, 32481, 9, 32482, 32483, 32484, 12, 32485, 32486, 32487, 15, 32488, 32489, 17, 32491, 18, 32491, 32493, 32494, 22, 21, 64967, 64961, 9, 18, 64976, 64979, 32487, 22, 32508, 32513, 32491, 27, 36, 32515, 64966, 32482, 39, 32516, 32522
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OFFSET
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1,1
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COMMENTS
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Sequences like this are more naturally considered with the first nonzero term in position 1. But this sequence would then match A000027 for its first 32478 terms.
This sequence has exactly 37025 terms (of positive index). a(37025) = 0, so an attempt to calculate a(37026) would refer to itself.
Without the convention that a(n) = 0 for n <= -32478, this sequence would have exactly 24 terms (of positive index), since computing a(25) refers to a(-64942).
If 32478 in this sequence's definition is replaced by any larger number congruent to 5 mod 7, the behavior is essentially the same, though the quasilinear part (see Formula section) lasts longer.
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LINKS
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FORMULA
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If the index is between 67 and 32479 (inclusive), then a(7n) = 7n+2, a(7n+1) = 7n+32480, a(7n+2) = 7n+32482, a(7n+3) = 7, a(7n+4) = 2n+65001, a(7n+5) = n+64949, a(7n+6) = 32476.
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MATHEMATICA
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a[n_] := a[n] = If[n <= 0, Max[0, n + 2^15 - 290], a[n - a[n - 1]] + a[n - a[n - 2]] + a[n - a[n - 3]]]; Array[a, 42] (* Robert G. Wilson v, Mar 19 2017 *)
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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EXTENSIONS
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Formula and definition corrected by Nathan Fox, Mar 18 2017
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STATUS
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approved
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