A112033 -id:A112033 - cp's OEIS frontend

A112034 1 / (A010684(n)/A016116(n+5) - 1/A112033(n)).

6, 24, 12, 48, 24, 96, 48, 192, 96, 384, 192, 768, 384, 1536, 768, 3072, 1536, 6144, 3072, 12288, 6144, 24576, 12288, 49152, 24576, 98304, 49152, 196608, 98304, 393216, 19660, 8, 786432, 393216, 1572864, 786432, 3145728, 1572864, 6291456

Offset: 0

Reinhard Zumkeller, Aug 27 2005

nonn

a(n) = 3*2^A052938(n).

Cf. A112030, A112031, A112032.

A016116 a(n) = 2^floor(n/2).

Original entry on oeis.org

1, 1, 2, 2, 4, 4, 8, 8, 16, 16, 32, 32, 64, 64, 128, 128, 256, 256, 512, 512, 1024, 1024, 2048, 2048, 4096, 4096, 8192, 8192, 16384, 16384, 32768, 32768, 65536, 65536, 131072, 131072, 262144, 262144, 524288, 524288, 1048576, 1048576, 2097152

Offset: 0

N. J. A. Sloane, Dec 11 1999

Powers of 2 doubled up. The usual OEIS policy is to omit the duplicates in such cases (when this would become A000079). This is an exception.
Number of symmetric compositions of n: e.g., 5 = 2+1+2 = 1+3+1 = 1+1+1+1+1 so a(5) = 4; 6 = 3+3 = 2+2+2 = 1+4+1 = 2+1+1+2 = 1+2+2+1 = 1+1+2+1+1 = 1+1+1+1+1+1 so a(6) = 8. - Henry Bottomley, Dec 10 2001
This sequence is the number of digits of each term of A061519. - Dmitry Kamenetsky, Jan 17 2009
Starting with offset 1 = binomial transform of [1, 1, -1, 3, -7, 17, -41, ...]; where A001333 = (1, 1, 3, 7, 17, 41, ...). - Gary W. Adamson, Mar 25 2009
a(n+1) is the number of symmetric subsets of [n]={1,2,...,n}. A subset S of [n] is symmetric if k is an element of S implies (n-k+1) is an element of S. - Dennis P. Walsh, Oct 27 2009
INVERT and inverse INVERT transforms give A006138, A039834(n-1).
The Kn21 sums, see A180662, of triangle A065941 equal the terms of this sequence. - Johannes W. Meijer, Aug 15 2011
First differences of A027383. - Jason Kimberley, Nov 01 2011
Run lengths in A079944. - Jeremy Gardiner, Nov 21 2011
Number of binary palindromes (A006995) between 2^(n-1) and 2^n (for n>1). - Hieronymus Fischer, Feb 17 2012
Pisano period lengths: 1, 1, 4, 1, 8, 4, 6, 1, 12, 8, 20, 4, 24, 6, 8, 1, 16, 12, 36, 8, ... . - R. J. Mathar, Aug 10 2012
Range of row n of the Circular Pascal array of order 4. - Shaun V. Ault, May 30 2014
a(n) is the number of permutations of length n avoiding both 213 and 312 in the classical sense which are breadth-first search reading words of increasing unary-binary trees. For more details, see the entry for permutations avoiding 231 at A245898. - Manda Riehl, Aug 05 2014
Also, the decimal representation of the diagonal from the origin to the corner (and from the corner to the origin except for the initial term) of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 190", based on the 5-celled von Neumann neighborhood when initialized with a single black (ON) cell at stage zero. - Robert Price, May 10 2017
a(n + 1) + n - 1, n > 0, is the number of maximal subsemigroups of the monoid of partial order-preserving or -reversing mappings on a set with n elements. See the East et al. link. - James Mitchell and Wilf A. Wilson, Jul 21 2017
Number of symmetric stairs with n cells. A stair is a snake polyomino allowing only two directions for adjacent cells: east and north. See A005418. - Christian Barrientos, May 11 2018
For n >= 4, a(n) is the exponent of the group of the Gaussian integers in a reduced system modulo (1+i)^(n+2). See A302254. - Jianing Song, Jun 27 2018
a(n) is the number of length-(n+1) binary sequences, denoted , with s(1)=1 and with s(i+1)=s(i) for odd i. - Dennis P. Walsh, Sep 06 2018
a(n+1) is the number of subsets of {1,2,..,n} in which all differences between successive elements of subsets are even.  For example, for n = 7, a(6) = 8 and the 8 subsets are {7}, {1,7}, {3,7}, {5,7}, {1,3,7}, {1,5,7}, {3,5,7}, {1,3,5,7}.  For odd differences between elements see Comment in A000045 (Fibonacci numbers). - Enrique Navarrete, Jul 01 2020
Also, the number of walks of length n on the graph x--y--z, starting at x. - Sean A. Irvine, May 30 2025

			For n=5 the a(5)=4 symmetric subsets of [4] are {1,4}, {2,3}, {1,2,3,4} and the empty set. - _Dennis P. Walsh_, Oct 27 2009
For n=5 the a(5)=4 length-6 binary sequences are <1,1,0,0,0,0>, <1,1,0,0,1,1>, <1,1,1,1,0,0> and <1,1,1,1,1,1>. - _Dennis P. Walsh_, Sep 06 2018

Vincenzo Librandi, Table of n, a(n) for n = 0..5000
Shaun V. Ault and Charles Kicey, Counting paths in corridors using circular Pascal arrays, Discrete Mathematics, Volume 332, Oct 06 2014, Pages 45-54.
Shaun V. Ault and Charles Kicey, Counting paths in corridors using circular Pascal arrays, arXiv:1407.2197 [math.CO], 2014.
Arvind Ayyer, Amritanshu Prasad, and Steven Spallone, Odd partitions in Young's lattice, arXiv:1601.01776 [math.CO], 2016. See Theorem 6 p. 12.
Paul Barry, On Integer-Sequence-Based Constructions of Generalized Pascal Triangles, J. Integer Sequ., Vol. 9 (2006), Article 06.2.4.
Francesco Battistoni and Giuseppe Molteni, An elementary proof for a generalization of a Pohst's inequality, arXiv:2101.06163 [math.NT], 2021.
Johann Cigler, Some remarks and conjectures related to lattice paths in strips along the x-axis, arXiv:1501.04750 [math.CO], 2015.
Johann Cigler, Recurrences for certain sequences of binomial sums in terms of (generalized) Fibonacci and Lucas polynomials, arXiv:2212.02118 [math.NT], 2022.
Emeric Deutsch, Problem 1633, Math. Mag., 74 #5 (2001), p. 403.
James East, Jitender Kumar, James D. Mitchell, and Wilf A. Wilson, Maximal subsemigroups of finite transformation and partition monoids, arXiv:1706.04967 [math.GR], 2017.
A. Goupil, H. Cloutier, and F. Nouboud, Enumeration of polyominoes inscribed in a rectangle Discrete Applied Mathematics 158(2010), pp. 2014-2023.
S. Heubach and T. Mansour, Counting rises, levels and drops in compositions, arXiv:math/0310197 [math.CO], 2003.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1067
D. Levin, L. Pudwell, M. Riehl, and A. Sandberg, Pattern Avoidance on k-ary Heaps, Slides of Talk, 2014.
D. Merlini, F. Uncini and M. C. Verri, A unified approach to the study of general and palindromic compositions, Integers 4 (2004), A23, 26 pp.
Agustín Moreno Cañadas, Hernán Giraldo, and Robinson Julian Serna Vanegas, Some integer partitions induced by orbits of Dynkin type, Far East Journal of Mathematical Sciences (FJMS), Vol. 101, No. 12 (2017), pp. 2745-2766.
Laurent Noé, Spaced seed design on profile HMMs for precise HTS read-mapping efficient sliding window product on the matrix semi-group, in Rapide Bilan 2012-2013, Laurent, LIFL, Université Lille 1 - INRIA Journées au vert 11 et 12 juin 2013, Laurent, Année 2012-2013.
Valentin Ovsienko, Villes paires et impaires (Oddtown and Eventown) I, Images des Mathématiques, CNRS, 2013 (in French).
Dennis Walsh, Notes on symmetric subsets of {1, 2, ..., n}
A. Yajima, How to calculate the number of stereoisomers of inositol-homologs, Bull. Chem. Soc. Jpn. 2014, 87, 1260-1264 | doi:10.1246/bcsj.20140204. See Tables 1 and 2 (and text). - _N. J. A. Sloane_, Mar 26 2015
Index to divisibility sequences
Index entries for linear recurrences with constant coefficients, signature (0,2).

Cf. A006995, A057148, A079944, A112030, A112033.
a(n) = A094718(3, n).
Cf. A001333.
See A052955 for partial sums (without the initial term).
A000079 gives the odd-indexed terms of a(n).
The following sequences are all essentially the same, in the sense that they are simple transformations of each other, with A029744 = {s(n), n>=1}, the numbers 2^k and 3*2^k, as the parent: A029744 (s(n)); A052955 (s(n)-1), A027383 (s(n)-2), A354788 (s(n)-3), A347789 (s(n)-4), A209721 (s(n)+1), A209722 (s(n)+2), A343177 (s(n)+3), A209723 (s(n)+4); A060482, A136252 (minor differences from A354788 at the start); A354785 (3*s(n)), A354789 (3*s(n)-7). The first differences of A029744 are 1,1,1,2,2,4,4,8,8,... which essentially matches eight sequences: A016116, A060546, A117575, A131572, A152166, A158780, A163403, A320770. The bisections of A029744 are A000079 and A007283. - N. J. A. Sloane, Jul 14 2022

List([0..45],n->2^Int(n/2)); # Muniru A Asiru, Apr 03 2018

[2^Floor(n/2): n in [0..50]]; // Vincenzo Librandi, Aug 16 2011

A016116:= proc(n): 2^floor(n/2) end: seq(A016116(n), n=0..42); # Dennis P. Walsh, Oct 27 2009

Table[ 2^Floor[n/2], {n, 0, 42}] (* Robert G. Wilson v, Jun 05 2004 *)
With[{c=2^Range[0,30]},Riffle[c,c]] (* Harvey P. Dale, Jan 23 2015 *)
CoefficientList[Series[(1+x)/(1-2*x^2), {x, 0, 50}], x] (* Stefano Spezia, Sep 07 2018 *)

makelist(2^floor(n/2), n, 0, 50); /* Martin Ettl, Oct 17 2012 */

PARI
```
a(n)=if(n<0,0,2^(n\2))
```

def A016116(n): return 1 << n//2 # Chai Wah Wu, Jun 07 2022

def A016116():
    x, y = -1, 0
    while True:
        yield -x
        x, y = x + y, x - y
a = A016116(); [next(a) for i in range(40)]  # Peter Luschny, Jul 11 2013

a(n) = a(n-1)*a(n-2)/a(n-3) = 2*a(n-2) = 2^A004526(n).
G.f.: (1+x)/(1-2*x^2).
a(n) = (1/2 + sqrt(1/8))*sqrt(2)^n + (1/2 - sqrt(1/8))*(-sqrt(2))^n. - Ralf Stephan, Mar 11 2003
E.g.f.: cosh(sqrt(2)*x) + sinh(sqrt(2)*x)/sqrt(2). - Paul Barry, Jul 16 2003
The signed sequence (-1)^n*2^floor(n/2) has a(n) = (sqrt(2))^n(1/2 - sqrt(2)/4) + (-sqrt(2))^n(1/2 + sqrt(2)/4). It is the inverse binomial transform of A000129(n-1). - Paul Barry, Apr 21 2004
Diagonal sums of A046854. a(n) = Sum_{k=0..n} binomial(floor(n/2), k). - Paul Barry, Jul 07 2004
a(n) = a(n-2) + 2^floor((n-2)/2). - Paul Barry, Jul 14 2004
a(n) = Sum_{k=0..floor(n/2)} binomial(floor(n/2), floor(k/2)). - Paul Barry, Jul 15 2004
E.g.f.: cosh(asinh(1) + sqrt(2)*x)/sqrt(2). - Michael Somos, Feb 28 2005
a(n) = Sum_{k=0..n} A103633(n,k). - Philippe Deléham, Dec 03 2006
a(n) = 2^(n/2)*((1 + (-1)^n)/2 + (1-(-1)^n)/(2*sqrt(2))). - Paul Barry, Nov 12 2009
a(n) = 2^((2*n - 1 + (-1)^n)/4). - Luce ETIENNE, Sep 20 2014

A010684 Period 2: repeat (1,3); offset 0.

Original entry on oeis.org

1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1

Offset: 0

N. J. A. Sloane

Hankel transform is [1,-8,0,0,0,0,0,0,0,0,...]. - Philippe Deléham, Mar 29 2007
Binomial transform gives [1,4,8,16,32,64,...] (A151821(n+1)). - Philippe Deléham, Sep 17 2009
Continued fraction expansion of (3+sqrt(21))/6. - Klaus Brockhaus, May 04 2010
Positive sum of the coordinates from the image of the point (1,-2) after n 90-degree rotations about the origin. - Wesley Ivan Hurt, Jul 06 2013
This sequence can be generated by an infinite number of formulas having the form a^(b*n) mod c where a is congruent to 3 mod 4 and b is any odd number. If a is congruent to 3 mod 4 then c can be 4; if a is also congruent to 3 mod 8 then c can be 8. For example: a(n)= 15^(3*n) mod 4, a(n) = 19^(5*n) mod 4, a(n) = 19^(5*n) mod 8. - Gary Detlefs, May 19 2014
This sequence is also the unsigned periodic Schick sequence for p = 5. See the Schick reference, p. 158, for p = 5.- Wolfdieter Lang, Apr 03 2020
Digits following the decimal point when 1/3 is converted to base 5. - Jamie Robert Creasey, Oct 15 2021
Decimal expansion of 13/99. - Stefano Spezia, Feb 09 2025

			0.131313131313131313131313131313131313131313131...

Carl Schick, Trigonometrie und unterhaltsame Zahlentheorie, Bokos Druck, Zürich, 2003 (ISBN 3-9522917-0-6). Tables 3.1 to 3.10, for odd p = 3..113 (with gaps), pp. 158-166.

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

Cf. A112030, A112033, A176014 (decimal expansion of (3+sqrt(21))/6).

[seq (modp((2*n+1),4),n=0..80)]; # Zerinvary Lajos, Nov 30 2006

Table[2-(-1)^n, {n, 0, 100}] (* Wesley Ivan Hurt, Mar 24 2014 *)
PadRight[{},120,{1,3}] (* Harvey P. Dale, Mar 11 2025 *)

a(n)=1+n%2*2 \\ Charles R Greathouse IV, Dec 28 2011

def A010684(n): return 3 if n&1 else 1 # Chai Wah Wu, Jan 17 2023

[power_mod(3, n, 8)for n in range(0, 81)] # Zerinvary Lajos, Nov 24 2009

From Paul Barry, Apr 29 2003: (Start)
a(n) = 2-(-1)^n.
G.f.: (1+3x)/((1-x)(1+x)).
E.g.f.: 2*exp(x) - exp(-x). (End)
a(n) = 2*A153643(n) - A153643(n+1). - Paul Curtz, Dec 30 2008
a(n) = 3^(n mod 2). - Jaume Oliver Lafont, Mar 27 2009
a(n) = 7^n mod 4. - Vincenzo Librandi, Feb 07 2011
a(n) = 1 + 2*(n mod 2). - Wesley Ivan Hurt, Jul 06 2013
a(n) = A000034(n) + A000035(n). - James Spahlinger, Feb 14 2016

A084964 Follow n+2 by n. Also solution of a(n+2)=a(n)+1, a(0)=2, a(1)=0.

Original entry on oeis.org

2, 0, 3, 1, 4, 2, 5, 3, 6, 4, 7, 5, 8, 6, 9, 7, 10, 8, 11, 9, 12, 10, 13, 11, 14, 12, 15, 13, 16, 14, 17, 15, 18, 16, 19, 17, 20, 18, 21, 19, 22, 20, 23, 21, 24, 22, 25, 23, 26, 24, 27, 25, 28, 26, 29, 27, 30, 28, 31, 29, 32, 30, 33, 31, 34, 32, 35, 33, 36, 34, 37, 35, 38, 36, 39

Offset: 0

Michael Somos, Jun 15 2003

Stefano Spezia, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
Index entries for two-way infinite sequences

Cf. A030451, A097065, A152832.

Cf. A217764(1,n) = a(n+2).

import Data.List (transpose)
a084964 n = a084964_list !! n
a084964_list = concat $ transpose [[2..], [0..]]
-- Reinhard Zumkeller, Apr 06 2015

&cat[ [n+2, n]: n in [0..37] ]; // Klaus Brockhaus, Nov 23 2009

A084964:=n->floor(n/2)+1+(-1)^n; seq(A084964(k), k=0..100); # Wesley Ivan Hurt, Nov 08 2013

lst={}; a=1; Do[a=n-a; AppendTo[lst, a], {n, 0, 100}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 14 2008 *)
Table[{n,n-2},{n,2,40}]//Flatten (* or *) LinearRecurrence[{1,1,-1},{2,0,3},80] (* Harvey P. Dale, Sep 12 2021 *)

PARI
```
a(n)=n\2-2*(n%2)+2
```

G.f.: (2-2x+x^2)/((1-x)(1-x^2)).
a(2n+1)=n. a(2n)=n+2. a(n+2)=a(n)+1. a(n)=-a(-3-n).
a(n) = floor(n/2) + 1 + (-1)^n. - Reinhard Zumkeller, Aug 27 2005
A112032(n)=2^a(n); A112033(n)=3*2^a(n); a(n)=A109613(n+2)-A052938(n). - Reinhard Zumkeller, Aug 27 2005
a(n) = n + 1 - a(n-1) (with a(0)=2). - Vincenzo Librandi, Aug 08 2010
a(n) = floor(n/2)*3 - floor((n-1)/2)*2. - Ross La Haye, Mar 27 2013
a(n) = 3*n - 3 - 5*floor((n-1)/2). - Wesley Ivan Hurt, Nov 08 2013
a(n) = (3 + 5*(-1)^n + 2*n)/4. - Wolfgang Hintze, Dec 13 2014
E.g.f.: ((4 + x)*cosh(x) - (1 - x)*sinh(x))/2. - Stefano Spezia, Jul 01 2023

First part of definition adjusted to match offset by Klaus Brockhaus, Nov 23 2009

A112030 a(n) = (2 + (-1)^n) * (-1)^floor(n/2).

Original entry on oeis.org

3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1, -3, -1, 3, 1

Offset: 0

Reinhard Zumkeller, Aug 27 2005

The fractions A112031(n)/A112032(n) give the partial sums of a(n)/floor((n+4)/2).

Sum of the two Cartesian coordinates from the image of the point (2,1) after n 90-degree counterclockwise rotations about the origin. - Wesley Ivan Hurt, Jul 06 2013

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

Cf. A010684, A016116, A112031, A112032, A112033.

A112030 := proc(n)
        (2 + (-1)^n) * (-1)^floor(n/2) ;
end proc: # R. J. Mathar, Jul 09 2013

LinearRecurrence[{0, -1}, {3, 1}, 100] (* Jean-François Alcover, Nov 24 2020 *)

a(n)=[3,1,-3,-1][n%4+1] \\ Charles R Greathouse IV, Aug 21 2011

def A112030(n): return (3, 1, -3, -1)[n&3] # Chai Wah Wu, Jan 31 2023

a(n) = A010684(n+1) * (-1)^floor(n/2).

O.g.f.: (3+x)/(1+x^2). - R. J. Mathar, Jan 09 2008

A112032 Denominator of 3/4 + 1/4 - 3/8 - 1/8 + 3/16 + 1/16 - 3/32 - 1/32 + 3/64 ...

Original entry on oeis.org

4, 1, 8, 2, 16, 4, 32, 8, 64, 16, 128, 32, 256, 64, 512, 128, 1024, 256, 2048, 512, 4096, 1024, 8192, 2048, 16384, 4096, 32768, 8192, 65536, 16384, 131072, 32768, 262144, 65536, 524288, 131072, 1048576, 262144, 2097152, 524288, 4194304, 1048576

Offset: 0

Reinhard Zumkeller, Aug 27 2005

Denominator of partial sums of A112030(n)/A016116(n+4), numerators = A112031;
A112031(n)/a(n) - 2/3 = (-1)^floor(n/2) / A112033(n);
lim_{n->infinity} A112031(n)/a(n) = 2/3.

G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part One, Chap. 4, Sect. 1, Problem 148.

Vincenzo Librandi, Table of n, a(n) for n = 0..3000
Index entries for linear recurrences with constant coefficients, signature (0,2).

Cf. A016116, A112030, A112031, A112033.

[2^(Floor(n/2) + 1 + (-1)^n): n in [0..50]]; // Vincenzo Librandi, Aug 17 2011

LinearRecurrence[{0,2},{4,1},50] (* following conjecture in Formula field above *) (* Harvey P. Dale, Dec 21 2014 *)

m=50; v=concat([4,1], vector(m-2)); for(n=3, m, v[n]=2*v[n-2]); v \\ G. C. Greubel, Nov 08 2018

a(n) = 2^(floor(n/2) + 1 + (-1)^n) = 2^A084964(n).
Conjectures from Colin Barker, Apr 05 2013: (Start)
a(n) = 2*a(n-2).
G.f.: (x+4) / (1-2*x^2). (End)

a(21) corrected by Vincenzo Librandi, Aug 17 2011

A112031 Numerator of 3/4 + 1/4 - 3/8 - 1/8 + 3/16 + 1/16 - 3/32 - 1/32 + 3/64 + ....

Original entry on oeis.org

3, 1, 5, 1, 11, 3, 21, 5, 43, 11, 85, 21, 171, 43, 341, 85, 683, 171, 1365, 341, 2731, 683, 5461, 1365, 10923, 2731, 21845, 5461, 43691, 10923, 87381, 21845, 174763, 43691, 349525, 87381, 699051, 174763, 1398101, 349525, 2796203, 699051, 5592405

Offset: 0

Reinhard Zumkeller, Aug 27 2005

Numerator of partial sums of A112030(n)/A016116(n+4), denominators = A112032;
a(n)/A112032(n) - 2/3 = (-1)^floor(n/2) / A112033(n);
lim_{n->infinity} a(n)/A112032(n) = 2/3.

G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part One, Chap. 4, Sect. 1, Problem 148.

Vincenzo Librandi, Table of n, a(n) for n = 0..3000
Index entries for linear recurrences with constant coefficients, signature (0,1,0,2).

Cf. A016116, A112030, A112032, A112033, A001045 (bisections).

[(2^(Floor(n/2) + 2 + (-1)^n) + (-1)^Floor(n/2)) / 3: n in [0..50]]; // Vincenzo Librandi, Aug 17 2011

LinearRecurrence[{0,1,0,2},{3,1,5,1},50] (* Harvey P. Dale, Dec 31 2017 *)

m=50; v=concat([3,1,5,1], vector(m-4)); for(n=5, m, v[n]=v[n-2] +2*v[n-4]); v \\ G. C. Greubel, Nov 08 2018

a(n) = (2^(floor(n/2) + 2 + (-1)^n) + (-1)^floor(n/2)) / 3.
From Colin Barker, Apr 05 2013: (Start)
a(n) = a(n-2) + 2*a(n-4);
g.f.: (2*x^2+x+3) / ((1+x^2)*(1-2*x^2)). (End)

a(22) corrected by Vincenzo Librandi, Aug 17 2011

cp's OEIS Frontend

A112034 1 / (A010684(n)/A016116(n+5) - 1/A112033(n)).

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A016116 a(n) = 2^floor(n/2).

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A010684 Period 2: repeat (1,3); offset 0.

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A084964 Follow n+2 by n. Also solution of a(n+2)=a(n)+1, a(0)=2, a(1)=0.

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A112030 a(n) = (2 + (-1)^n) * (-1)^floor(n/2).

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A112032 Denominator of 3/4 + 1/4 - 3/8 - 1/8 + 3/16 + 1/16 - 3/32 - 1/32 + 3/64 ...

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