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A143025
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Period length 4: repeat 1,8,2,8.
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4
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1, 8, 2, 8, 1, 8, 2, 8, 1, 8, 2, 8, 1, 8, 2, 8, 1, 8, 2, 8, 1, 8, 2, 8, 1, 8, 2, 8, 1, 8, 2, 8, 1, 8, 2, 8, 1, 8, 2, 8, 1, 8, 2, 8, 1, 8, 2, 8, 1, 8, 2, 8, 1, 8, 2, 8, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Numerator of 1/n^2-1/(3n)^2 if n>0.
This can be generated from the transitions between principal quantum numbers n and 3n in the Hydrogen series: A005563(2), A061037(6), A061039(9), A061041(12), A061043(15), A061045(18), A061047(21), A061049(24),... (The mention of A005563(2) is somewhat a fluke to maintain the periodic pattern.)
Related to the continued fraction of (12*sqrt(55)-72)/19 = 0.89444115.. = 0+1/(1+1/(8+1/(2+...))). - R. J. Mathar, Jun 27 2011
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients, signature (0,0,0,1).
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FORMULA
| a(n+4) = a(n), starting 1,8,2,8.
a(n) = (1/24)*(61*(n mod 4)-17*((n+1) mod 4)+55*((n+2) mod 4)-23*((n+3) mod 4)), with n>=0. [From Paolo P. Lava (paoloplava(AT)gmail.com), Feb 23 2010]
G.f.: (1+8*x+2*x^2+8*x^3)/(1-x^4).
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PROG
| (PARI) a(n)=[1, 8, 2, 8][n%4+1] \\ Charles R Greathouse IV, Jun 02 2011
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CROSSREFS
| Cf. A045944, A144437.
Sequence in context: A132716 A134724 A021551 * A085967 A163960 A143531
Adjacent sequences: A143022 A143023 A143024 * A143026 A143027 A143028
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KEYWORD
| nonn,easy
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Oct 13 2008
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EXTENSIONS
| Partially edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 10 2008
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