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A002081
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Numbers congruent to {2, 4, 8, 16} mod 20.
(Formerly M1113 N0426)
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4
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2, 4, 8, 16, 22, 24, 28, 36, 42, 44, 48, 56, 62, 64, 68, 76, 82, 84, 88, 96, 102, 104, 108, 116, 122, 124, 128, 136, 142, 144, 148, 156, 162, 164, 168, 176, 182, 184, 188, 196, 202, 204, 208, 216, 222, 224, 228, 236, 242, 244, 248, 256, 262, 264, 268, 276, 282
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| First differences are periodic, cf. A000689.
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REFERENCES
| C. Babbage, On the Determination of the General Term of a New Class of Infinite Series, Trans. Camb. Phil. Soc., 2 (1827), 217-225 (see p. 220).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
| G.f.: 2*(1+2*x^2+2*x^3)/((1-x)^2*(1+x^2)). - S. Plouffe
a(n) = Sum_{k=0..n}{1/6*(8*(k mod 4)-((k+1) mod 4)+2*((k+2) mod 4)+11*((k+3) mod 4))}-4. - Paolo P. Lava, Aug 01 2007
a(n + 4) = a(n) + 20 for n > 3. - Reinhard Zumkeller, Sep 15 2011
a(n) = 5*n+(1/2)*(3+(-1)^n)*(-1)^(n(n+1)/2). - Bruno Berselli, Sep 15 2011
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MAPLE
| A002081:=2*(1+2*z**2+2*z**3)/(z**2+1)/(z-1)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Flatten[Table[20n + {2, 4, 8, 16}, {n, 0, 14}]] (* Alonso del Arte, Nov 30 2011 *)
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PROG
| (PARI) a(n)=5*n+[2, -1, -2, 1][(n%4)+1] - Ralf Stephan, Jun 08 2005
(Haskell)
a002081 n = a002081_list
a002081_list = filter ((`elem` [2, 4, 8, 16]) . (`mod` 20)) [1..]
-- Reinhard Zumkeller, Sep 15 2011
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CROSSREFS
| Cf. A002082, A008587.
Sequence in context: A196871 A001856 * A102039 A045844 A063108 A161140
Adjacent sequences: A002078 A002079 A002080 * A002082 A002083 A002084
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Jul 31 2000
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