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A028356
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Simple periodic sequence underlying clock sequence A028354.
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12
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1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Contribution from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 15 2010: (Start)
Continued fraction expansion of (28+sqrt(2730))/56.
Decimal expansion of 1112/9009.
Partial sums of 1 followed by A130151.
First differences of A028357. (End)
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REFERENCES
| Zdenek Horsky, "Prazsky Orloj" ["The Astronomical Clock of Prague", in Czech], Panorama, Prague, 1988, pp. 76-78.
M. Krizek, A. Solcova and L. Somer, Construction of Sindel sequences, Comment. Math. Univ. Carolin., 48 (2007), 373-388.
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LINKS
| N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).
Index to sequences with linear recurrences with constant coefficients, signature (1,0,-1,1).
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FORMULA
| Sum of any six successive terms is 15.
Coefficients in expansion of (1 + 2x + 3x^2 + 4x^3 + 3x^4 + 2x^5)/(1 - x^6).
a(n)=(1/3)*{[cos(2*n*Pi/3) + 1/2]*[1 + (-1)^n] + 2*[cos(2*(n + 5)*Pi/3) + 1/2]*[1 + (-1)^(n + 5)] + 3*[cos(2*(n + 4)*Pi/3) + 1/2]*[1 + (-1)^(n + 4)] + [4*cos(2*(n + 3)*Pi/3) + 1/2]*[1 + (-1)^(n + 3)] + [3*cos(2*(n + 2)*Pi/3) + 1/2]*[1 + (-1)^(n + 2)] + [2*cos(2*(n + 1)*Pi/3) + 1/2]*[1 + (-1)^(n + 1)]} - Paolo P. Lava (paoloplava(AT)gmail.com), Oct 09 2006
a(n)=1/3*[n mod 6+(n+1) mod 6+(n+2) mod 6] - Paolo P. Lava (paoloplava(AT)gmail.com), Oct 09 2006
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MATHEMATICA
| CoefficientList[ Series[(1 + 2x + 3x^2 + 4x^3 + 3x^4 + 2x^5)/(1 - x^6), {x, 0, 85}], x]
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PROG
| (MAGMA) &cat[ [1, 2, 3, 4, 3, 2]: n in [1..20] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 15 2010]
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CROSSREFS
| Cf. A000034, A068073, A028354.
Cf. A177924 (decimal expansion of (28+sqrt(2730))/56), A130151 (repeat 1, 1, 1, -1, -1, -1), A028357 (partial sums of A028356). [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 15 2010]
Sequence in context: A008287 A017859 A171456 * A073791 A030340 A122453
Adjacent sequences: A028353 A028354 A028355 * A028357 A028358 A028359
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Additional comments from Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 01 2002
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