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A028356
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Simple periodic sequence underlying clock sequence A028354.
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14
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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
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listen;
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OFFSET
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0,2
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COMMENTS
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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
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Zdeněk Horský, "Pražský orloj" ("The Astronomical Clock of Prague", in Czech), Panorama, Prague, 1988, pp. 76-78.
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LINKS
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FORMULA
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Sum of any six successive terms is 15.
G.f.: (1 + 2*x + 3*x^2 + 4*x^3 + 3*x^4 + 2*x^5)/(1 - x^6).
a(n) = a(n-1) - a(n-3) + a(n-4) for n>3.
a(n) = (15 - cos(n*Pi) - 8*cos(n*Pi/3))/6. (End)
E.g.f.: (15*exp(x) - exp(-x) - 8*cos(sqrt(3)*x/2)*(sinh(x/2) + cosh(x/2)))/6. - Ilya Gutkovskiy, Jun 23 2016
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MAPLE
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MATHEMATICA
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CoefficientList[ Series[(1 + 2x + 3x^2 + 4x^3 + 3x^4 + 2x^5)/(1 - x^6), {x, 0, 85}], x]
LinearRecurrence[{1, 0, -1, 1}, {1, 2, 3, 4}, 120] (* or *) PadRight[{}, 120, {1, 2, 3, 4, 3, 2}] (* Harvey P. Dale, Apr 15 2016 *)
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PROG
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(Sage)
def A():
a, b, c, d = 1, 2, 3, 4
while True:
yield a
a, b, c, d = b, c, d, a + (d - b)
(Python)
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CROSSREFS
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KEYWORD
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nonn,easy,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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