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A168198
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a(n) = 3*n - a(n-1) + 1 with n > 1, a(1)=1.
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2
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1, 6, 4, 9, 7, 12, 10, 15, 13, 18, 16, 21, 19, 24, 22, 27, 25, 30, 28, 33, 31, 36, 34, 39, 37, 42, 40, 45, 43, 48, 46, 51, 49, 54, 52, 57, 55, 60, 58, 63, 61, 66, 64, 69, 67, 72, 70, 75, 73, 78, 76, 81, 79, 84, 82, 87, 85, 90, 88, 93, 91, 96, 94, 99, 97, 102, 100, 105, 103, 108
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OFFSET
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1,2
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COMMENTS
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Alternately add 5 and subtract 2, starting with 1. Apparently this was a test question: Find the next two numbers after 1,6,4,9,7,12,10. - N. J. A. Sloane, Dec 18 2010
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LINKS
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FORMULA
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Sum_{n>=1} (-1)^(n+1)/a(n) = 1/3 + Pi/(6*sqrt(3)) + log(3)/2. - Amiram Eldar, Feb 23 2023
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EXAMPLE
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For n = 2, a(2) = 3*2 - a[2-1] + 1 = 6 - a[1] + 1 = 6 - 1 + 1 = 6.
For n = 3, a(3) = 3*3 - a[3-1] + 1 = 9 - a[2] + 1 = 9 - 6 + 1 = 4.
For n = 4, a(4) = 3*4 - a[4-1] + 1 = 12 - a[3] + 1 = 12 - 4 + 1 = 9.
... (End)
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MAPLE
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a:= proc(n) option remember: if n = 1 then 1 elif n >= 2 then 3*n - procname(n-1) + 1 fi; end:
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MATHEMATICA
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PROG
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(Magma) I:=[1, 6, 4]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..60]]; // Vincenzo Librandi, Feb 28 2012
(GAP) a:=[1];; for n in [2..80] do a[n]:=3*n-a[n-1]+1; od; a; # Muniru A Asiru, Mar 20 2018
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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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