|
Search: id:A002081
|
|
|
| A002081 |
|
Numbers congruent to {2, 4, 8, 16} mod 20.
(Formerly M1113 N0426)
|
|
+0
3
|
|
| 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; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
First differences are periodic.
|
|
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).
|
|
LINKS
|
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.
|
|
FORMULA
|
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 (ppl(AT)spl.at), Aug 01 2007
|
|
MAPLE
|
A002081:=2*(1+2*z**2+2*z**3)/(z**2+1)/(z-1)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]
|
|
PROGRAM
|
(PARI) a(n)=5*n+[2, -1, -2, 1][(n%4)+1] - Ralf Stephan, Jun 08 2005
|
|
CROSSREFS
|
Cf. A002082.
Sequence in context: A045776 A102252 A001856 this_sequence A102039 A045844 A063108
Adjacent sequences: A002078 A002079 A002080 this_sequence A002082 A002083 A002084
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
More terms from Larry Reeves (larryr(AT)acm.org), Jul 31 2000
|
|
|
Search completed in 0.002 seconds
|
