A028357 -id:A028357 - cp's OEIS frontend

A028358 Partial sums of A028357.

1, 4, 10, 20, 33, 48, 64, 82, 103, 128, 156, 186, 217, 250, 286, 326, 369, 414, 460, 508, 559, 614, 672, 732, 793, 856, 922, 992, 1065, 1140, 1216, 1294, 1375, 1460, 1548, 1638, 1729, 1822, 1918, 2018, 2121

Offset: 0

N. J. A. Sloane

Index entries for linear recurrences with constant coefficients, signature (3,-3,0,3,-3,1).

LinearRecurrence[{3,-3,0,3,-3,1},{1,4,10,20,33,48},50] (* Harvey P. Dale, Jun 14 2021 *)
Table[(9 + 72n + 30n^2 + 32Cos[(n + 1)Pi/3] - (-1)^n)/24, {n, 0, 40}] (* Greg Dresden, Jun 22 2021 *)

G.f.: ( -1-x-x^2-2*x^3 ) / ( (1+x)*(x^2-x+1)*(x-1)^3 ). - R. J. Mathar, Dec 15 2015

a(n) = (9 + 72*n + 30*n^2 + 32*cos((n + 1)*Pi/3) - (-1)^n)/24. - Greg Dresden, Jun 22 2021

A028356 Simple periodic sequence underlying clock sequence A028354.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

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)

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

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).

Cf. A000034, A028354, A068073, A118382, A118383.

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

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

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

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 *)

def A028356(n): return (1,2,3,4,3,2)[n%6] # Chai Wah Wu, Apr 18 2024

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

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).
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
a(n) = abs(((n+3) mod 6)-3) + 1. - Daniel Jiménez, Jan 14 2023

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

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A028358 Partial sums of A028357.

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A028356 Simple periodic sequence underlying clock sequence A028354.

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