A007484 -id:A007484 - cp's OEIS frontend

A007482 a(n) is the number of subsequences of [ 1, ..., 2n ] in which each odd number has an even neighbor.

1, 3, 11, 39, 139, 495, 1763, 6279, 22363, 79647, 283667, 1010295, 3598219, 12815247, 45642179, 162557031, 578955451, 2061980415, 7343852147, 26155517271, 93154256107, 331773802863, 1181629920803, 4208437368135

Offset: 0

N. J. A. Sloane

The even neighbor must differ from the odd number by exactly one.
If we defined this sequence by the recurrence (a(n) = 3*a(n-1) + 2*a(n-2)) that it satisfies, we could prefix it with an initial 0.
a(n) equals term (1,2) in M^n, M = the 3 X 3 matrix [1,1,2; 1,0,1; 2,1,1]. - Gary W. Adamson, Mar 12 2009
a(n) equals term (2,2) in M^n, M = the 3 X 3 matrix [0,1,0; 1,3,1; 0,1,0]. - Paul Barry, Sep 18 2009
From Gary W. Adamson, Aug 06 2010: (Start)
Starting with "1" = INVERT transform of A002605: (1, 2, 6, 16, 44, ...).
Example: a(3) = 39 = (16, 6, 2, 1) dot (1, 1, 3, 11) = (16 + 6 + 6 + 11). (End)
Pisano periods: 1, 1, 4, 1, 24, 4, 48, 2, 12, 24, 30, 4, 12, 48, 24, 4,272, 12, 18, 24, ... . - R. J. Mathar, Aug 10 2012
A007482 is also the number of ways of tiling a 3 X n rectangle with 1 X 1 squares, 2 X 2 squares and 2 X 1 (vertical) dominoes. - R. K. Guy, May 20 2015
With offset 1 (a(0) = 0, a(1) = 1) this is a divisibility sequence. - Michael Somos, Jun 03 2015
Number of elements of size 2^(-n) in a fractal generated by the second-order reversible cellular automaton, rule 150R (see the reference and the link). - Yuriy Sibirmovsky, Oct 04 2016
a(n) is the number of compositions (ordered partitions) of n into parts 1 (of three kinds) and 2 (of two kinds). - Joerg Arndt, Oct 05 2016
a(n) equals the number of words of length n over {0,1,2,3,4} in which 0 and 1 avoid runs of odd lengths. - Milan Janjic, Jan 08 2017
Start with a single cell at coordinates (0, 0), then iteratively subdivide the grid into 2 X 2 cells and remove the cells that have two '1's in their modulo 3 coordinates. a(n) is the number of cells after n iterations. Cell configuration converges to a fractal with approximate dimension 1.833. - Peter Karpov, Apr 20 2017
This is the Lucas sequence U(P=3,Q=-2), and hence for n>=0, a(n+2)/a(n+1) equals the continued fraction 3 + 2/(3 + 2/(3 + 2/(3 + ... + 2/3))) with n 2's. - Greg Dresden, Oct 06 2019

			G.f. = 1 + 3*x + 11*x^2 + 39*x^3 + 139*x^4 + 495*x^5 + 1763*x^6 + ...
From _M. F. Hasler_, Jun 16 2019: (Start)
For n = 0, (1, ..., 2n) = () is the empty sequence, which is equal to its only subsequence, which satisfies the condition voidly, whence a(0) = 1.
For n = 1, (1, ..., 2n) = (1, 2); among the four subsequences {(), (1), (2), (1,2)} only (1) does not satisfy the condition, whence a(1) = 3.
For n = 2, (1, ..., 2n) = (1, 2, 3, 4); among the sixteen subsequences {(), ..., (1,2,3,4)}, the 5 subsequences (1), (3), (1,3), (2,3,4) and (1,2,3,4) do not satisfy the condition, whence a(2) = 16 - 5 = 11.
(End)

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002, p. 439.

T. D. Noe, Table of n, a(n) for n = 0..200
Paul Barry, Notes on Riordan arrays and lattice paths, arXiv:2504.09719 [math.CO], 2025. See pp. 13, 29.
Alexander Burstein and Opel Jones, Enumeration of Dumont permutations avoiding certain four-letter patterns, arXiv:2002.12189 [math.CO], 2020.
R. K. Guy and William O. J. Moser, Numbers of subsequences without isolated odd members, Fibonacci Quarterly, 34, No. 2, 152-155 (1996). Math. Rev. 97d:11017.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 442
Peter Karpov, InvMem, Item 26
Peter Karpov, Illustration of initial terms (n = 1..8)
Yuriy Sibirmovsky, A fractal with number of elements described by a(n)
Index entries for linear recurrences with constant coefficients, signature (3,2).

Row sums of triangle A073387.
Cf. A000045, A000129, A001045, A007455, A007481, A007483, A007484, A015518, A201000 (prime subsequence), A052913 (binomial transform), A026597 (inverse binomial transform).
Cf. A206776.

a007482 n = a007482_list !! (n-1)
a007482_list = 1 : 3 : zipWith (+)
               (map (* 3) $ tail a007482_list) (map (* 2) a007482_list)
-- Reinhard Zumkeller, Oct 21 2015

I:=[1,3]; [n le 2 select I[n] else 3*Self(n-1) + 2*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 16 2018

a := n -> `if`(n=0, 1, 3^n*hypergeom([(1-n)/2,-n/2], [-n], -8/9)):
seq(simplify(a(n)), n = 0..23); # Peter Luschny, Jun 28 2017

a[n_]:=(MatrixPower[{{1,4},{1,2}},n].{{1},{1}})[[2,1]]; Table[a[n],{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2010 *)
LinearRecurrence[{3,2},{1,3},30] (* Harvey P. Dale, May 25 2013 *)
a[ n_] := Module[ {m = n + 1, s = 1}, If[ m < 0, {m, s} = -{m, (-2)^m}]; s SeriesCoefficient[ x / (1 - 3 x - 2 x^2), {x, 0, m}]]; (* Michael Somos, Jun 03 2015 *)
a[ n_] := With[{m = n + 1}, If[ m < 0, (-2)^m a[ -m], Expand[((3 + Sqrt[17])/2)^m - ((3 - Sqrt[17])/2)^m ] / Sqrt[17]]]; (* Michael Somos, Oct 13 2016 *)

a(n) := if n=0 then 1 elseif n=1 then 3 else 3*a(n-1)+2*a(n-2);
makelist(a(n),n,0,12); /* Emanuele Munarini, Jun 28 2017 */

{a(n) = 2*imag(( (3 + quadgen(68)) / 2)^(n+1))}; /* Michael Somos, Jun 03 2015 */

[lucas_number1(n,3,-2) for n in range(1, 25)] # Zerinvary Lajos, Apr 22 2009

G.f.: 1/(1-3*x-2*x^2).
a(n) = 3*a(n-1) + 2*a(n-2).
a(n) = (ap^(n+1)-am^(n+1))/(ap-am), where ap = (3+sqrt(17))/2 and am = (3-sqrt(17))/2.
Let b(0) = 1, b(k) = floor(b(k-1)) + 2/b(k-1); then, for n>0, b(n) = a(n)/a(n-1). - Benoit Cloitre, Sep 09 2002
The Hankel transform of this sequence is [1,2,0,0,0,0,0,0,0,...]. - Philippe Deléham, Nov 21 2007
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, k)2^k*3^(n-2k). - Paul Barry, Apr 23 2005
a(n) = Sum_{k=0..n} A112906(n,k). - Philippe Deléham, Nov 21 2007
a(n) = - a(-2-n) * (-2)^(n+1) for all n in Z. - Michael Somos, Jun 03 2015
If c = (3 + sqrt(17))/2, then c^n = (A206776(n) + sqrt(17)*a(n-1)) / 2. - Michael Somos, Oct 13 2016
a(n) = 3^n*hypergeom([(1-n)/2,-n/2], [-n], -8/9) for n>=1. - Peter Luschny, Jun 28 2017
a(n) = round(((sqrt(17) + 3)/2)^(n+1)/sqrt(17)). The distance of the argument from the nearest integer is about 1/2^(n+3). - M. F. Hasler, Jun 16 2019
E.g.f.: (1/17)*exp(3*x/2)*(17*cosh(sqrt(17)*x/2) + 3*sqrt(17)*sinh(sqrt(17)*x/2)). - Stefano Spezia, Oct 07 2019
a(n) = (sqrt(2)*i)^n * ChebyshevU(n, -3*i/(2*sqrt(2))). - G. C. Greubel, Dec 24 2021
G.f.: 1/(1 - 3*x - 2*x^2) = Sum_{n >= 0} x^n * Product_{k = 1..n} (k + 2*x + 2)/(1 + k*x) (a telescoping series). Cf. A015518. - Peter Bala, May 08 2024

A104934 Expansion of (1-x)/(1 - 3x - 2x^2).

Original entry on oeis.org

1, 2, 8, 28, 100, 356, 1268, 4516, 16084, 57284, 204020, 726628, 2587924, 9217028, 32826932, 116914852, 416398420, 1483024964, 5281871732, 18811665124, 66998738836, 238619546756, 849856117940, 3026807447332, 10780134577876, 38394018628292, 136742325040628, 487015012378468, 1734529687216660

Offset: 0

Creighton Dement, Mar 29 2005

A floretion-generated sequence relating A007482, A007483, A007484. Inverse is A046717. Inverse of Fibonacci(3n+1), A033887. Binomial transform is A052984. Inverse binomial transform is A006131. Note: the conjectured relation 2*a(n) = A007482(n) + A007483(n-1) is a result of the FAMP identity dia[I] + dia[J] + dia[K] = jes + fam
Floretion Algebra Multiplication Program, FAMP Code: 1dia[I]tesseq[A*B] with A = - .25'i + .25'j + .25'k - .25i' + .25j' + .25k' - .25'ii' + .25'jj' + .25'kk' + .25'ij' + .25'ik' + .25'ji' + .25'jk' + .25'ki' + .25'kj' - .25e and B = + 'i + i' + 'ji' + 'ki' + e
a(n) is also the number of ways to build a (2 x 2 x n)-tower using (2 X 1 X 1)-bricks (see Exercise 3.15 in Aigner's book). - Vania Mascioni (vmascioni(AT)bsu.edu), Mar 09 2009
a(n) is the number of compositions of n when there are 2 types of 1 and 4 types of other natural numbers. - Milan Janjic, Aug 13 2010
Pisano period lengths: 1, 1, 4, 1, 24, 4, 48, 1, 12, 24, 30, 4, 12, 48, 24, 1,272, 12, 18, 24, ... - R. J. Mathar, Aug 10 2012

M. Aigner, A Course in Enumeration, Springer, 2007, p.103.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
I. M. Gessel and Ji Li, Compositions and Fibonacci identities, J. Int. Seq. 16 (2013) 13.4.5
Index entries for linear recurrences with constant coefficients, signature (3,2)

Cf. A006131, A007482 (partial sums), A007483, A007484, A033887, A046717, A052984, A055099, A104935, A122542.

# Following the Pari implementation.
function a(n)
   F = BigInt[0 1; 2 3]
   Fn = F^n * [1; 2]
   Fn[1, 1]
end # Peter Luschny, Jan 06 2019

m:=35; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1 - x)/(1 - 3*x - 2*x^2)); // Vincenzo Librandi, Jul 13 2018

a := proc(n) option remember; `if`(n < 2, [1, 2][n+1], (3*a(n-1) + 2*a(n-2))) end:
seq(a(n), n=0..28); # Peter Luschny, Jan 06 2019

LinearRecurrence[{3, 2}, {1, 2}, 40] (* Vincenzo Librandi, Jul 13 2018 *)
CoefficientList[Series[(1-x)/(1-3x-2x^2),{x,0,40}],x] (* Harvey P. Dale, May 02 2019 *)

a(n)=([0,1; 2,3]^n*[1;2])[1,1] \\ Charles R Greathouse IV, Jun 20 2015

[(i*sqrt(2))^(n-1)*(i*sqrt(2)*chebyshev_U(n, -3*i/(2*sqrt(2))) - chebyshev_U(n-1, -3*i/(2*sqrt(2))) ) for n in (0..40)] # G. C. Greubel, Jun 27 2021

Define A007483(-1) = 1. Then 2*a(n) = A007482(n) + A007483(n-1) (conjecture);
  a(n+2) = 4*A007484(n) (thus 8*A007484(n) = A007482(n+2) + A007483(n+1));
  a(n+1) = 2*A055099(n);
  a(n+2) - a(n+1) - a(n) = A007484(n+1) - A007484(n).
a(0)=1, a(1)=2, a(n) = 3*a(n-1) + 2*a(n-2) for n > 1. - Philippe Deléham, Sep 19 2006
a(n) = Sum_{k=0..n} 2^k*A122542(n,k). - Philippe Deléham, Oct 08 2006
a(n) = ((17+sqrt(17))/34)*((3+sqrt(17))/2)^n + ((17-sqrt(17))/34)*((3-sqrt(17))/2)^n. - Richard Choulet, Nov 19 2008
a(n) = 2*a(n-1) + 4*Sum_{k=0..n-2} a(k) for n > 0. - Vania Mascioni (vmascioni(AT)bsu.edu), Mar 09 2009
G.f.: (1-x)/(1-3*x-2*x^2). - M. F. Hasler, Jul 12 2018
a(n) = (i*sqrt(2))^(n-1)*( i*sqrt(2)*ChebyshevU(n, -3*i/(2*sqrt(2))) - ChebyshevU(n-1, -3*i/(2*sqrt(2))) ). - G. C. Greubel, Jun 27 2021
E.g.f.: exp(3*x/2)*(sqrt(17)*cosh(sqrt(17)*x/2) + sinh(sqrt(17)*x/2))/sqrt(17). - Stefano Spezia, May 24 2024

A275183 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

Original entry on oeis.org

1, 2, 1, 5, 4, 2, 14, 16, 7, 4, 41, 64, 25, 12, 8, 122, 256, 89, 41, 21, 16, 365, 1024, 317, 141, 85, 37, 32, 1094, 4096, 1129, 482, 353, 181, 65, 64, 3281, 16384, 4021, 1651, 1465, 914, 389, 114, 128, 9842, 65536, 14321, 5653, 6081, 4603, 2386, 834, 200, 256, 29525

Offset: 1

R. H. Hardin, Jul 19 2016

Table starts
...1...2....5....14.....41.....122......365......1094.......3281........9842
...1...4...16....64....256....1024.....4096.....16384......65536......262144
...2...7...25....89....317....1129.....4021.....14321......51005......181657
...4..12...41...141....482....1651.....5653.....19356......66277......226937
...8..21...85...353...1465....6081....25241....104769.....434873.....1805057
..16..37..181...914...4603...23313...117916....596625....3018913....15274618
..32..65..389..2386..14643...90793...561044...3472521...21488129...132962186
..64.114..834..6228..46799..355258..2688402..20397794..154665843..1172975241
.128.200.1781.16249.149772.1392050.12931103.120384453.1120217646.10428404709
.256.351.3799.42451.479722.5466938.62408531.713359905.8156812360.93298660085

			Some solutions for n=4 k=4
..0..0..1..2. .0..1..1..2. .0..0..1..1. .0..0..1..2. .0..0..0..1
..2..2..0..1. .2..0..0..1. .2..2..0..0. .2..2..0..1. .1..2..2..0
..0..1..2..0. .1..2..2..2. .0..1..1..2. .1..1..2..2. .0..1..1..2
..2..0..1..2. .0..0..1..1. .2..0..0..1. .0..0..0..1. .2..2..0..0

R. H. Hardin, Table of n, a(n) for n = 1..364

Column 1 is A000079(n-2).
Column 2 is A005251(n+3).
Row 1 is A007051(n-1).
Row 2 is A000302(n-1).
Row 3 is A007484(n-1).

Empirical for column k:
k=1: a(n) = 2*a(n-1) for n>2
k=2: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
k=3: a(n) = 4*a(n-1) -6*a(n-2) +5*a(n-3) -a(n-4) -a(n-5) for n>8
k=4: [order 9] for n>12
k=5: [order 16] for n>21
k=6: [order 34] for n>39
k=7: [order 67] for n>73
Empirical for row n:
n=1: a(n) = 4*a(n-1) -3*a(n-2)
n=2: a(n) = 4*a(n-1)
n=3: a(n) = 3*a(n-1) +2*a(n-2)
n=4: a(n) = 2*a(n-1) +4*a(n-2) +3*a(n-3) for n>4
n=5: a(n) = 2*a(n-1) +7*a(n-2) +8*a(n-3) for n>5
n=6: a(n) = 2*a(n-1) +12*a(n-2) +19*a(n-3) -4*a(n-4) -12*a(n-5) -16*a(n-6) for n>7
n=7: [order 9] for n>10

A184761 T(n,k)=Half the number of nXk binary arrays with no 1 having an adjacent 1 both above and to its left.

Original entry on oeis.org

1, 2, 2, 4, 7, 4, 8, 25, 25, 8, 16, 89, 163, 89, 16, 32, 317, 1056, 1056, 317, 32, 64, 1129, 6847, 12397, 6847, 1129, 64, 128, 4021, 44391, 145778, 145778, 44391, 4021, 128, 256, 14321, 287802, 1713803, 3110914, 1713803, 287802, 14321, 256, 512, 51005, 1865917

Offset: 1

R. H. Hardin Jan 21 2011

Table starts
...1......2........4...........8.............16...............32
...2......7.......25..........89............317.............1129
...4.....25......163........1056...........6847............44391
...8.....89.....1056.......12397.........145778..........1713803
..16....317.....6847......145778........3110914.........66363023
..32...1129....44391.....1713803.......66363023.......2568513843
..64...4021...287802....20148584.....1415755252......99419347147
.128..14321..1865917...236878817....30202770902....3848174315295
.256..51005.12097367..2784890782...644326291402..148949599913987
.512.181657.78431296.32740859687.13745636657969.5765325542821919

			Some solutions for 4X3
..1..1..0....1..0..0....0..1..1....0..0..0....0..0..1....1..0..0....0..0..0
..0..0..0....0..0..1....0..0..1....0..0..1....1..0..0....0..1..0....1..0..1
..1..1..0....1..0..1....1..1..0....0..0..1....1..1..0....0..0..1....1..0..1
..0..0..0....0..0..0....0..0..1....1..1..0....0..1..0....1..0..0....0..1..0

R. H. Hardin, Table of n, a(n) for n = 1..760

Column 2 is A007484(n-1) and 1/2 A055099 and 1/4 A104934(n+1)

A208269 T(n,k)=Number of nXk 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.

Original entry on oeis.org

1, 2, 2, 4, 7, 4, 8, 25, 25, 8, 16, 89, 161, 89, 16, 32, 317, 1033, 1033, 317, 32, 64, 1129, 6631, 11929, 6631, 1129, 64, 128, 4021, 42563, 137845, 137845, 42563, 4021, 128, 256, 14321, 273205, 1592731, 2867739, 1592731, 273205, 14321, 256, 512, 51005, 1753657

Offset: 1

R. H. Hardin Feb 24 2012

Table starts
...1.....2.......4.........8..........16............32..............64
...2.....7......25........89.........317..........1129............4021
...4....25.....161......1033........6631.........42563..........273205
...8....89....1033.....11929......137845.......1592731........18403423
..16...317....6631....137845.....2867739......59655167......1240971177
..32..1129...42563...1592731....59655167....2234126207.....83670667271
..64..4021..273205..18403423..1240971177...83670667271...5641457245533
.128.14321.1753657.212644499.25815151595.3133560234217.380372051615157

			Some solutions for n=4 k=3
..0..1..0....0..0..1....0..0..0....0..1..0....0..0..0....0..0..0....0..0..0
..0..0..0....0..1..0....0..1..1....1..0..1....0..1..1....1..0..1....1..0..1
..1..1..1....1..1..1....1..0..1....0..0..0....1..0..1....0..1..1....1..0..1
..1..0..0....0..0..0....0..1..0....1..1..0....0..1..1....0..0..1....1..0..1

R. H. Hardin, Table of n, a(n) for n = 1..759

Column 2 is A007484(n-1)

A007481 Number of subsequences of [ 1,...,n ] in which each even number has an odd neighbor.

Original entry on oeis.org

1, 2, 3, 7, 11, 25, 39, 89, 139, 317, 495, 1129, 1763, 4021, 6279, 14321, 22363, 51005, 79647, 181657, 283667, 646981, 1010295, 2304257, 3598219, 8206733, 12815247, 29228713, 45642179, 104099605, 162557031, 370756241, 578955451, 1320467933

Offset: 0

N. J. A. Sloane

A055099(n) = a(2*n+1) - a(2*n) = a(2*(n+1)) - a(2*n+1). - Reinhard Zumkeller, Oct 25 2015

			For n=2, there are the following three subsequences of [1,2] with the desired property: empty, [1], [1,2].
For n=3, there are the following seven subsequences of [1,2,3] with the desired property: empty, [1], [3], [1,2], [2,3], [1,3], [1,2,3].

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 0..400
R. K. Guy and W. O. J. Moser, Numbers of subsequences without isolated odd members, Fibonacci Quarterly 34:2 (1996), pp. 152-155.
Index entries for linear recurrences with constant coefficients, signature (0, 3, 0, 2).

Cf. A007455, A007482, A007484, A055099.

a007481 n = a007481_list !! n
a007481_list = 1 : 2 : 3 : 7 : zipWith (+)
               (map (* 3) $ drop 2 a007481_list) (map (* 2) a007481_list)
-- Reinhard Zumkeller, Oct 25 2015

LinearRecurrence[{0,3,0,2},{1,2,3,7},40] (* Harvey P. Dale, Feb 29 2012 *)

a(n)=([0,1,0,0; 0,0,1,0; 0,0,0,1; 2,0,3,0]^n*[1;2;3;7])[1,1] \\ Charles R Greathouse IV, Mar 02 2016

a(n) = 3*a(n-2) + 2*a(n-4).

G.f.: (x^3+2*x+1)/(-2*x^4-3*x^2+1). - Harvey P. Dale, Feb 29 2012

More terms from James Sellers, Dec 24 1999

A007455 Number of subsequences of [ 1,...,n ] in which each odd number has an even neighbor.

Original entry on oeis.org

1, 1, 3, 5, 11, 17, 39, 61, 139, 217, 495, 773, 1763, 2753, 6279, 9805, 22363, 34921, 79647, 124373, 283667, 442961, 1010295, 1577629, 3598219, 5618809, 12815247, 20011685, 45642179, 71272673, 162557031, 253841389, 578955451, 904069513

Offset: 0

N. J. A. Sloane, Mira Bernstein

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n=0..400
R. K. Guy, William O. J. Moser, Numbers of subsequences without isolated odd members, Fibonacci Quarterly, 34, No. 2, 152-155 (1996).
Index entries for linear recurrences with constant coefficients, signature (0,3,0,2).

Cf. A007481, A007482, A007484.

a007455_list = 1 : 1 : 3 : 5 : zipWith (+)
   (map (* 2) a007455_list) (map (* 3) $ drop 2 a007455_list)
a007455 n = a007455_list !! n
-- Reinhard Zumkeller, Jul 16 2012

CoefficientList[Series[(-1-x-2 x^3)/(-1+3 x^2+2 x^4),{x,0,40}],x]  (* Harvey P. Dale, Feb 18 2011 *)
LinearRecurrence[{0,3,0,2},{1,1,3,5},40] (* Harvey P. Dale, Feb 10 2015 *)

A007455(n)=[n%2*2+3,1]*([3,1;2,0]^(n\2-1))[,1] \\ M. F. Hasler, Jun 19 2019

a(n) = 3*a(n-2) + 2*a(n-4).

G.f. = (1 + x + 2 x^3)/(1 - 3 x^2 - 2 x^4). - Harvey P. Dale, Feb 18 2011, edited by M. F. Hasler, Jun 19 2019

cp's OEIS Frontend

A007482 a(n) is the number of subsequences of [ 1, ..., 2n ] in which each odd number has an even neighbor.

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A104934 Expansion of (1-x)/(1 - 3*x - 2*x^2).

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A275183 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

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A184761 T(n,k)=Half the number of nXk binary arrays with no 1 having an adjacent 1 both above and to its left.

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A208269 T(n,k)=Number of nXk 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.

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A007481 Number of subsequences of [ 1,...,n ] in which each even number has an odd neighbor.

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A007455 Number of subsequences of [ 1,...,n ] in which each odd number has an even neighbor.

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A104934 Expansion of (1-x)/(1 - 3x - 2x^2).