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A028356 Simple periodic sequence underlying clock sequence A028354. 14
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; text; internal format)
OFFSET

0,2

COMMENTS

From Klaus Brockhaus, 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)

REFERENCES

Zdeněk Horský, "Pražský orloj" ("The Astronomical Clock of Prague", in Czech), Panorama, Prague, 1988, pp. 76-78.

LINKS

Table of n, a(n) for n=0..105.

Michal Křížek, Alena Šolcová and Lawrence Somer, Construction of Šindel sequences, Comment. Math. Univ. Carolin., 48 (2007), 373-388.

N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).

Index entries for linear recurrences with constant coefficients, signature (1,0,-1,1).

FORMULA

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) = (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, Oct 09 2006

a(n) = [n mod 6+(n+1) mod 6+(n+2) mod 6]/3. - Paolo P. Lava, Oct 09 2006

From Wesley Ivan Hurt, Jun 23 2016: (Start)

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

MAPLE

A028356:=n->[1, 2, 3, 4, 3, 2][(n mod 6)+1]: seq(A028356(n), n=0..100); # Wesley Ivan Hurt, Jun 23 2016

MATHEMATICA

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 *)

PROG

(MAGMA) &cat [[1, 2, 3, 4, 3, 2]^^20]; // Klaus Brockhaus, May 15 2010

(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)

A028356 = A(); [A028356.next() for n in range(106)] # Peter Luschny, Jul 26 2014

CROSSREFS

Cf. A000034, A028354, A068073.

Cf. A177924 (decimal expansion of (28+sqrt(2730))/56), A130151 (repeat 1, 1, 1, -1, -1, -1), A028357 (partial sums of A028356). - Klaus Brockhaus, May 15 2010

Sequence in context: A008287 A017859 A171456 * A232244 A260644 A073791

Adjacent sequences:  A028353 A028354 A028355 * A028357 A028358 A028359

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Additional comments from Robert G. Wilson v, Mar 01 2002

STATUS

approved

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Last modified July 17 16:38 EDT 2019. Contains 325107 sequences. (Running on oeis4.)