A007877 -id:A007877 - cp's OEIS frontend

A271832 Period 12 zigzag sequence: repeat [0,1,2,3,4,5,6,5,4,3,2,1].

0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1

Offset: 0

Wesley Ivan Hurt, Apr 15 2016

a(n)/36 is the probability that the sum shown after rolling a pair of standard dice is 1+(n mod 12). - Mathew Englander, Jul 11 2022

Decimal expansion of 37037/3000003. - Elmo R. Oliveira, Mar 03 2024

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

Period k zigzag sequences: A000035 (k=2), A007877 (k=4), A260686 (k=6), A266313 (k=8), A271751 (k=10), this sequence (k=12), A279313 (k=14), A279319 (k=16), A158289 (k=18).

Cf. A010677, A011655, A110551.

&cat[[0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1]: n in [0..10]];

A271832:=n->[0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1][(n mod 12)+1]: seq(A271832(n), n=0..300);

CoefficientList[Series[x*(1 + x + x^2 + x^3 + x^4 + x^5)/(1 - x + x^6 - x^7), {x, 0, 100}], x]

lista(nn) = for(n=0, nn, print1(abs(n-12*round(n/12)), ", ")); \\ Altug Alkan, Apr 15 2016

G.f.: x*(1 + x + x^2 + x^3 + x^4 + x^5)/(1 - x + x^6 - x^7).
a(n) = a(n-1) - a(n-6) + a(n-7) for n>6.
a(n) = abs(n - 12*round(n/12)).
a(n) = Sum_{i=1..n} (-1)^floor((i-1)/6).
a(2n) = a(10n) = 2*A260686(n), a(2n+1) = A110551(n).
a(3n) = 3*A007877(n), a(4n) = a(8n) = 4*A011655(n).
a(6n) = A010677(n) = 6*A000035(n).
a(n) = a(n-12) for n >= 12. - Wesley Ivan Hurt, Sep 07 2022

A266313 Period 8 zigzag sequence; repeat [0, 1, 2, 3, 4, 3, 2, 1].

Original entry on oeis.org

0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4, 3

Offset: 0

Wesley Ivan Hurt, Dec 26 2015

Decimal expansion of 1111/90009. - Elmo R. Oliveira, Mar 03 2024

			G.f. = x + 2*x^2 + 3*x^3 + 4*x^4 + 3*x^5 + 2*x^6 + x^7 + x^9 + ... - _Michael Somos_, Feb 27 2020

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

Period k zigzag sequences: A000035 (k=2), A007877 (k=4), A260686 (k=6), this sequence (k=8), A271751 (k=10), A271832 (k=12), A279313 (k=14), A279319 (k=16), A158289 (k=18).

Cf. A084101.

&cat[[0, 1, 2, 3, 4, 3, 2, 1]: n in [0..10]];

A266313:=n->[0, 1, 2, 3, 4, 3, 2, 1][(n mod 8)+1]: seq(A266313(n), n=0..100);

CoefficientList[Series[x*(1 + x + x^2 + x^3)/(1 - x + x^4 - x^5), {x, 0, 100}], x]

x='x+O('x^100); concat(0, Vec(x*(1+x+x^2+x^3)/(1-x+x^4-x^5))) \\ Altug Alkan, Dec 29 2015

{a(n) = abs((n+4)\8*8-n)}; /* Michael Somos, Feb 27 2020 */

G.f.: x*(1+x+x^2+x^3)/(1-x+x^4-x^5).
a(n) = a(n-1) - a(n-4) + a(n-5) for n > 4.
a(n) = Sum_{i = 1..n} (-1)^floor((i-1)/4).
a(2n) = 2*A007877(n); a(2n+1) = A084101(n).
a(n) = abs(n - 8*round(n/8)). - Jon E. Schoenfield, Jan 01 2016
Euler transform of length 8 sequence [2, 0, 0, -2, 0, 0, 0, 1]. - Michael Somos, Feb 27 2020
a(n) = a(n-8) for n >= 8. - Wesley Ivan Hurt, Sep 07 2022

A279319 Period 16 zigzag sequence: repeat [0,1,2,3,4,5,6,7,8,7,6,5,4,3,2,1].

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5

Offset: 0

Wesley Ivan Hurt, Dec 09 2016

Decimal expansion of 11111111/900000009. - Elmo R. Oliveira, Feb 20 2024

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

Period k zigzag sequences: A000035 (k=2), A007877 (k=4), A260686 (k=6), A266313 (k=8), A271751 (k=10), A271832 (k=12), A279313 (k=14), this sequence (k=16), A158289 (k=18).

&cat[[0, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1]: n in [0..5]];

PadRight[{}, 120, {0, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1}] (* Vincenzo Librandi, Dec 10 2016 *)
With[{k = 16}, Table[Min[Abs[# - k], #] &@ Mod[n, k], {n, 0, 120}]] (* or *)
CoefficientList[Series[x (1 + x) (1 + x^2) (1 + x^4)/((1 - x) (1 + x^8)), {x, 0, 120}], x] (* Michael De Vlieger, Dec 10 2016 *)

def A279319(n): return (0,1,2,3,4,5,6,7,8,7,6,5,4,3,2,1)[n&15] # Chai Wah Wu, Mar 02 2023

a(n) = abs(n - 16*round(n/16)).
G.f.: x*(1 + x)*(1 + x^2)*(1 + x^4)/((1 - x)*(1 + x^8)). - Ilya Gutkovskiy, Dec 10 2016
a(n) = a(n-1)-a(n-8)+a(n-9). - Wesley Ivan Hurt, Nov 18 2021
a(n) = a(n-16) for n >= 16. - Wesley Ivan Hurt, Sep 07 2022

A098178 Expansion of (1+x)(1-x+x^2)/((1-x)(1+x^2)).

Original entry on oeis.org

1, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2

Offset: 0

Paul Barry, Aug 30 2004

Transform of A011782 under the Chebyshev mapping g(x)-> ((1-x^2)/(1+x^2)) * g(x/(1+x^2)).
Binomial transform is A098179.
Multiplicative with a(2) = 0, a(2^e) = 2 if e >= 2, a(p^e) = 1. [David W. Wilson, Jun 12 2005]
1, followed by period 4, repeat [1, 0, 1, 2]. [Joerg Arndt, Jan 06 2014]

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

Cf. A007877, A098179.

[1] cat &cat [[1, 0, 1, 2]^^30]; // Wesley Ivan Hurt, Jul 07 2016

with(numtheory); A098178:=n->signum(n)-1+sqrt((n-2)^2 mod 8); seq(A098178(n), n=0..100); # Wesley Ivan Hurt, Jan 04 2014

CoefficientList[Series[(1+x)(1-x+x^2)/((1-x)(1+x^2)),{x,0,120}],x] (* or *) PadRight[{1},120,{2,1,0,1}] (* Harvey P. Dale, May 01 2013 *)
Table[Sign[n] - 1 + Sqrt[Mod[(n - 2)^2, 8]], {n, 0, 100}] (* Wesley Ivan Hurt, Jan 04 2014 *)
Join[{1},LinearRecurrence[{1, -1, 1},{1, 0, 1},104]] (* Ray Chandler, Sep 03 2015 *)

G.f.: (1+x)(1-x+x^2)/((1-x)(1+x^2)).
a(n) = 1 + cos(Pi*n/2) - 0^n.
a(n) = a(n-1) - a(n-2) + a(n-3) for n>2.
a(n) = A007877(n+2), n>0. Dirichlet g.f. (1-1/2^s+2/4^s)*zeta(s). - R. J. Mathar, Feb 24 2011
a(n) = sign(n) - 1 + sqrt((n-2)^2 mod 8). - Wesley Ivan Hurt, Jan 04 2014
a(n) = a(n-4) for n>4. - Wesley Ivan Hurt, Jul 07 2016
E.g.f.: exp(x) + cos(x) - 1. - Ilya Gutkovskiy, Jul 07 2016

A098181 Two consecutive odd numbers separated by multiples of four, repeated twice, between them, written in increasing order.

Original entry on oeis.org

1, 3, 4, 4, 5, 7, 8, 8, 9, 11, 12, 12, 13, 15, 16, 16, 17, 19, 20, 20, 21, 23, 24, 24, 25, 27, 28, 28, 29, 31, 32, 32, 33, 35, 36, 36, 37, 39, 40, 40, 41, 43, 44, 44, 45, 47, 48, 48, 49, 51, 52, 52, 53, 55, 56, 56, 57, 59, 60, 60, 61, 63, 64, 64, 65, 67, 68, 68, 69, 71, 72, 72

Offset: 0

Paul Barry, Aug 30 2004

Essentially partial sums of A007877.

a(n) is the number of odd coefficients of the q-binomial coefficient [n+2 choose 2]. (Easy to prove.) - Richard Stanley, Oct 12 2016

			G.f. = 1 + 3*x + 4*x^2 + 4*x^3 + 5*x^4 + 7*x^5 + 8*x^6 + 8*x^7 + 9*x^8 + ...

G. C. Greubel, Table of n, a(n) for n = 0..10000
P. Barry, On a Generalization of the Narayana Triangle, J. Int. Seq. 14 (2011) # 11.4.5.
Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).

Cf. A098180.

a:=[1,3,4,4];; for n in [5..80] do a[n]:=2*a[n-1]-2*a[n-2]+2*a[n-3] -a[n-4]; od; a; # G. C. Greubel, May 22 2019

R:=PowerSeriesRing(Integers(), 80); Coefficients(R!( (1+x)/((1-x)^2*(1+x^2)) )); // G. C. Greubel, May 22 2019

A:=seq((2*n+3 - cos(Pi*n/2) + sin(Pi*n/2))/2, n=0..50); \\ Bernard Schott, Jun 07 2019

Table[Floor[Binomial[n+3, 2]/2] -Floor[Binomial[n+1, 2]/2], {n, 0, 80}] (* or *) CoefficientList[Series[(1+x)/((1-x)^2*(1+x^2)), {x, 0, 80}], x] (* Michael De Vlieger, Oct 12 2016 *)

{a(n) = n\4*4 + [1, 3, 4, 4][n%4+1]}; /* Michael Somos, Sep 11 2014 */

((1+x)/((1-x)^2*(1+x^2))).series(x, 80).coefficients(x, sparse=False) # G. C. Greubel, May 22 2019

G.f.: (1+x)/((1-x)^2*(1+x^2)).
a(n) = ( (2*n+3) - cos(Pi*n/2) + sin(Pi*n/2) )/2.
a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4).
a(n) = floor(C(n+3, 2)/2)-floor(C(n+1, 2)/2). - Paul Barry, Jan 01 2005
a(4*n) = 4*n+1, a(4*n+1) = 4*n+3, a(4*n+2) = a(4*n+3) = 4*n+4. - Philippe Deléham, Apr 06 2007
Euler transform of length 4 sequence [ 3, -2, 0, 1]. - Michael Somos, Sep 11 2014
a(-3-n) = -a(n) for all n in Z. - Michael Somos, Sep 11 2014
a(n) = log_2(|A174882(n+2)|). [Barry] - R. J. Mathar, Aug 18 2017
a(n) = (2*n+3 - (-1)^ceiling(n/2))/2. - Wesley Ivan Hurt, Sep 29 2017

Name edited by G. C. Greubel, Jun 06 2019

A084104 A period 6 sequence.

Original entry on oeis.org

1, 4, 7, 7, 4, 1, 1, 4, 7, 7, 4, 1, 1, 4, 7, 7, 4, 1, 1, 4, 7, 7, 4, 1, 1, 4, 7, 7, 4, 1, 1, 4, 7, 7, 4, 1, 1, 4, 7, 7, 4, 1, 1, 4, 7, 7, 4, 1, 1, 4, 7, 7, 4, 1, 1, 4, 7, 7, 4, 1, 1, 4, 7, 7, 4, 1, 1, 4, 7, 7, 4, 1, 1, 4, 7, 7, 4, 1, 1, 4, 7, 7, 4, 1, 1, 4, 7, 7, 4, 1, 1, 4, 7, 7, 4, 1, 1, 4, 7, 7, 4, 1, 1, 4, 7

Offset: 0

Paul Barry, May 15 2003

Partial sums of A084103.

Index entries for linear recurrences with constant coefficients, signature (2,-2,1).

Cf. A084101, A007877.

PARI
```
{a(n)=[1, 4, 7, 7, 4, 1][n%6+1]}
```

a(n)=2*sqrt(3)*sin((n+5)*Pi/3)+4 \\ Jaume Oliver Lafont, Aug 27 2009

Euler transform of length 6 sequence [ 4, -3, -1, 0, 0, 1]. - Michael Somos, Nov 07 2006
G.f.: (1+x)^3/((1-x)(1+x^3)).
G.f.:(1+x)^2/((1-x)*(1-x+x^2)). - Jaume Oliver Lafont, Aug 27 2009

A293296 a(n) = 2*n^2 - floor(n/4).

Original entry on oeis.org

0, 2, 8, 18, 31, 49, 71, 97, 126, 160, 198, 240, 285, 335, 389, 447, 508, 574, 644, 718, 795, 877, 963, 1053, 1146, 1244, 1346, 1452, 1561, 1675, 1793, 1915, 2040, 2170, 2304, 2442, 2583, 2729, 2879, 3033, 3190, 3352, 3518, 3688, 3861, 4039, 4221, 4407, 4596

Offset: 0

Peter Luschny, Oct 08 2017

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).

Cf. A001105, A007877.

a := n -> 2*n^2 - floor(n/4): seq(a(n), n=0..48);

LinearRecurrence[{2, -1, 0, 1, -2, 1}, {0, 2, 8, 18, 31, 49}, 49]
Table[2n^2-Floor[n/4],{n,0,60}] (* Harvey P. Dale, Jan 08 2022 *)

a(n) = 2*n^2-n\4; \\ Altug Alkan, Oct 08 2017

def A293296(n): return (n**2<<1)-(n>>2) # Chai Wah Wu, Jan 26 2023

a(n) = [x^n] (-x*(2+4*x+4*x^2+3*x^3+3*x^4)/((x+1)*(x^2+1)*(x-1)^3)).
a(n) = n! [x^n] (3*exp(x)-exp(-x)+14*exp(x)*x+16*exp(x)*x^2-2*cos(x)-2*sin(x))/8.
a(n) = a(n-6) - 2*a(n-5) + a(n-4) - a(n-2) + 2*a(n-1) for n >= 6.
(-1)^n*(a(n+3) - 3*a(n+2) + 3*a(n+1) - a(n)) = sqrt(n^2 mod 8) = A007877(n).

A104563 A floretion-generated sequence relating to centered square numbers.

Original entry on oeis.org

0, 1, 3, 5, 8, 13, 19, 25, 32, 41, 51, 61, 72, 85, 99, 113, 128, 145, 163, 181, 200, 221, 243, 265, 288, 313, 339, 365, 392, 421, 451, 481, 512, 545, 579, 613, 648, 685, 723, 761, 800, 841, 883, 925, 968, 1013, 1059, 1105, 1152, 1201, 1251

Offset: 0

Creighton Dement, Mar 15 2005

Floretion Algebra Multiplication Program, FAMP Code: a(n) = 1vesrokseq[A*B] with A = - .5'i - .5i' + .5'ii' + .5e, B = + .5'ii' - .5'jj' + .5'kk' + .5e. RokType: Y[sqa.Findk()] = Y[sqa.Findk()] + Math.signum(Y[sqa.Findk()])*p (internal program code). Note: many slight variations of the "RokType" already exist, such that it has become difficult to assign them all names.

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-4,4,-3,1).

Cf. A001844, A004525, A104564, A098180, A059100, A010000, A047599, A007877.

LinearRecurrence[{3, -4, 4, -3, 1}, {0, 1, 3, 5, 8}, 60] (* Amiram Eldar, Dec 14 2024 *)

concat(0, Vec(x*(1 + x)*(1 - x + x^2) / ((1 - x)^3*(1 + x^2)) + O(x^40))) \\ Colin Barker, Apr 29 2019

G.f.: x*(1 + x^3)/((1 + x^2)*(1 - x)^3).
FAMP result: 2*a(n) + 2*A004525(n+1) = A104564(n) + a(n+1).
Superseeker results:
a(2*n+1) = A001844(n) = 2*n*(n+1) + 1 (Centered square numbers);
a(n+1) - a(n) = A098180(n) (Odd numbers with two times the odd numbers repeated in order between them);
a(n) + a(n+2) = A059100(n+1) = A010000(n+1);
a(n+2) - a(n) = A047599(n+1) (Numbers that are congruent to {0, 3, 4, 5} mod 8);
a(n+2) - 2*a(n+1) + a(n) = A007877(n+3) (Period 4 sequence with initial period (0, 1, 2, 1));
Coefficients of g.f.*(1-x)/(1+x) = convolution of this with A280560 gives A004525;
Coefficients of g.f./(1+x) = convolution of this with A033999 gives A054925.
a(n) = (1/2)*(n^2 + 1 - cos(n*Pi/2)). - Ralf Stephan, May 20 2007
From Colin Barker, Apr 29 2019: (Start)
a(n) = (2 - (-i)^n - i^n + 2*n^2) / 4 where i=sqrt(-1).
a(n) = 3*a(n-1) - 4*a(n-2) + 4*a(n-3) - 3*a(n-4) + a(n-5) for n>4. (End)
a(n) = A011848(n-1)+A011848(n+2). - R. J. Mathar, Sep 11 2019
Sum_{n>=1} 1/a(n) = Pi^2/48 + (Pi/2) * tanh(Pi/2) + (Pi/(4*sqrt(2)) * tanh(Pi/(2*sqrt(2)))). - Amiram Eldar, Dec 14 2024

Stephan's formula corrected by Bruno Berselli, Apr 29 2019

A155040 A symmetric (1,-1)-triangle.

Original entry on oeis.org

1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1

Offset: 0

Paul Barry, Jan 19 2009

Row sums are A007877(n+1). Diagonal sums are A155041.

			Triangle begins
.1,
.1, 1,
.1, -1, 1,
.1, -1, -1, 1,
.1, -1, 1, -1, 1,
.1, -1, 1, 1, -1, 1,
.1, -1, 1, -1, 1, -1, 1,
.1, -1, 1, -1, -1, 1, -1, 1,
.1, -1, 1, -1, 1, -1, 1, -1, 1,
.1, -1, 1, -1, 1, 1, -1, 1, -1, 1,
.1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1,
.1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1

Number triangle T(n,k)=sum{j=0..n, [j<=k]*[j<=n-k]*(-1)*(((-1)^(j+1)-0^(j+1))-((-1)^j-0^j))}.

A164360 Period 3: repeat [5, 4, 3].

Original entry on oeis.org

5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3

Offset: 0

Stephen Crowley, Aug 14 2009

From Klaus Brockhaus, May 29 2010: (Start)
Continued fraction expansion of (32+sqrt(1297))/13.
Decimal expansion of 181/333. (End)

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

Cf. A007877 (repeat 0,1,2,1), A068073 (repeat 1,2,3,2), A028356 (repeat 1,2,3,4,3,2), A130784 (repeat 1,3,2), A158289 (repeat 0,1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2,1).

Cf. A178566 (decimal expansion of (32+sqrt(1297))/13). [Klaus Brockhaus, May 29 2010]

[ n le 3 select 6-n else Self(n-3):n in [1..105] ]; // Klaus Brockhaus, Sep 17 2009

&cat [[5, 4, 3]^^30]; // Wesley Ivan Hurt, Jul 01 2016

seq(op([5, 4, 3]), n=0..50); # Wesley Ivan Hurt, Jul 01 2016

PadRight[{}, 100, {5, 4, 3}] (* Wesley Ivan Hurt, Jul 01 2016 *)

a(n) = 4+(-1)^n*((1/2+I*sqrt(3)/6)*((1+I*sqrt(3))/2)^n+(1/2-I*sqrt(3)/6)*((1-I*sqrt(3))/2)^n). [Corrected by Klaus Brockhaus, Sep 17 2009]
a(n) = 4+(1/3)*sqrt(3)*sin(2*n*Pi/3)+cos(2*n*Pi/3). [Corrected by Klaus Brockhaus, Sep 17 2009]
a(n) = a(n-3) for n > 2, with a(0) = 5, a(1) = 4, a(2) = 3.
G.f.: (5+4*x+3*x^2)/((1-x)*(1+x+x^2)). [Klaus Brockhaus, Sep 17 2009]
E.g.f.: 4*exp(x)+(1/3)*sqrt(3)*exp(-(1/2)*x)*sin((1/2)*x*sqrt(3))+exp(-(1/2)*x)*cos((1/2)*x*sqrt(3)).
a(n) = 4 + A057078(n). - Wesley Ivan Hurt, Jul 01 2016

Edited by Klaus Brockhaus, Sep 17 2009

Offset changed to 0 and formulas adjusted by Klaus Brockhaus, May 18 2010

cp's OEIS Frontend

A271832 Period 12 zigzag sequence: repeat [0,1,2,3,4,5,6,5,4,3,2,1].

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A266313 Period 8 zigzag sequence; repeat [0, 1, 2, 3, 4, 3, 2, 1].

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A279319 Period 16 zigzag sequence: repeat [0,1,2,3,4,5,6,7,8,7,6,5,4,3,2,1].

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A098178 Expansion of (1+x)(1-x+x^2)/((1-x)(1+x^2)).

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Maple

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Formula

A098181 Two consecutive odd numbers separated by multiples of four, repeated twice, between them, written in increasing order.

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Sage

Formula

Extensions

A084104 A period 6 sequence.

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PARI

PARI