A183256 Number of nX1 binary arrays with the number of 0-1 adjacencies equal to the number of 0-0 adjacencies

2, 1, 3, 3, 7, 8, 17, 26, 55, 89, 170, 298, 585, 1059, 1988, 3640, 6943, 12990, 24469, 45663, 86454, 163324, 309092, 582651, 1103457, 2092206, 3971963, 7529743, 14293584, 27163872, 51678766, 98293571, 187034535, 356132703, 678651768

Offset

1,1

Comments

Column 1 of A183262

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

a(n) = [x^n] f(n,x) where f(1,x) = 2*x, f(2,x) = x^3+x^2+2*x, and f(n,x) = (1-x^3)*f(n-2,x) + (x+x^2)*f(n-1,x) otherwise. - Robert Israel, Nov 13 2019

Example

All solutions for 5X1
..0....0....1....1....0....1....0
..0....1....0....1....0....1....0
..1....0....0....1....1....1....0
..1....0....0....0....0....1....1
..1....0....1....0....0....1....0

Maple

fx:= proc(n) option remember; expand((1-x^3)*procname(n-2)+(x+x^2)*procname(n-1)) end proc:
fx(0):= 0: fx(1):= 2*x: fx(2):= x^3 + x^2 + 2*x:
seq(coeff(fx(n), x, n), n=1..40); # Robert Israel, Nov 13 2019

Mathematica

fx[n_] := fx[n] = Expand[(1-x^3)*fx[n-2] + (x+x^2)*fx[n-1]];
fx[0] = 0; fx[1] = 2x; fx[2] = x^3 + x^2 + 2x;
Table[Coefficient[fx[n], x, n], {n, 1, 40}] (* Jean-François Alcover, Aug 29 2022, after Robert Israel *)

Crossrefs

Cf. A183262.

Sequence in context: A338417 A034399 A005292 * A328319 A307366 A249137

Adjacent sequences: A183253 A183254 A183255 * A183257 A183258 A183259

Keyword

nonn

Author

R. H. Hardin, Jan 03 2011

Status

approved