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A091999
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Numbers that are congruent to {2, 10} mod 12.
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18
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2, 10, 14, 22, 26, 34, 38, 46, 50, 58, 62, 70, 74, 82, 86, 94, 98, 106, 110, 118, 122, 130, 134, 142, 146, 154, 158, 166, 170, 178, 182, 190, 194, 202, 206, 214, 218, 226, 230, 238, 242, 250, 254, 262, 266, 274, 278, 286, 290, 298, 302, 310, 314, 322, 326, 334
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OFFSET
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1,1
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COMMENTS
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Numbers divisible by 2 but not by 3 or 4. - Robert Israel, Apr 24 2015
For n > 1, a(n) is representable as a sum of four but no fewer consecutive nonnegative integers, i.e., 10 = 1 + 2 + 3 + 4, 14 = 2 + 3 + 4 + 5, 22 = 4 + 5 + 6 + 7, etc. (see A138591). - Martin Renner, Mar 14 2016
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LINKS
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FORMULA
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G.f.: 2*x*(1+4*x+x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
a(n) = a(n-1) + a(n-2) - a(n-3); a(1)=2, a(2)=10, a(3)=14. - Harvey P. Dale, Jun 24 2013
E.g.f.: 2 + (6*x - 2)*cosh(x) + 2*(3*x - 2)*sinh(x). - Stefano Spezia, May 09 2021
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/(4*sqrt(3)). - Amiram Eldar, Dec 13 2021
E.g.f.: 2 + (6*x - 3)*exp(x) + exp(-x). - David Lovler, Aug 08 2022
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MAPLE
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MATHEMATICA
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Flatten[#+{2, 10}&/@(12*Range[0, 30])] (* or *) LinearRecurrence[{1, 1, -1}, {2, 10, 14}, 60] (* Harvey P. Dale, Jun 24 2013 *)
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PROG
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(Haskell)
a091999 n = a091999_list !! (n-1)
a091999_list = 2 : 10 : map (+ 12) a091999_list
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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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