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A047225
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Numbers that are congruent to {0, 1} mod 6.
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7
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0, 1, 6, 7, 12, 13, 18, 19, 24, 25, 30, 31, 36, 37, 42, 43, 48, 49, 54, 55, 60, 61, 66, 67, 72, 73, 78, 79, 84, 85, 90, 91, 96, 97, 102, 103, 108, 109, 114, 115, 120, 121, 126, 127, 132, 133, 138, 139, 144, 145, 150
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OFFSET
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1,3
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COMMENTS
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Expansion of 1/(1 + x + x^2 + x^3 + x^4 + x^5) = 1 - x + x^6 - x^7 + x^12 - x^13 + ... and the exponents are the terms of this sequence. - Gary W. Adamson, Apr 04 2011
Numbers k such that floor(k/2) = 3*floor(k/6). - Bruno Berselli, Oct 05 2017
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LINKS
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FORMULA
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O.g.f.: 1/(1+x) + 3/(-1+x)^2 + 4/(-1+x).
a(n) = a(n-2) + 6, n >= 2. (End)
Sum_{n>=2} (-1)^n/a(n) = sqrt(3)*Pi/12 + log(2)/3 + log(3)/4. - Amiram Eldar, Dec 13 2021
E.g.f.: 5 + (3*x - 4)*exp(x) - exp(-x). - David Lovler, Aug 25 2022
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MAPLE
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a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=a[n-2]+6 od: seq(a[n], n=0..50); # Zerinvary Lajos, Mar 16 2008
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MATHEMATICA
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{#, #+1}&/@(6Range[0, 30])//Flatten (* or *) LinearRecurrence[{1, 1, -1}, {0, 1, 6}, 60] (* Harvey P. Dale, Aug 24 2019 *)
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PROG
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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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EXTENSIONS
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STATUS
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approved
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