A207170 Number of 2 X n 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 0 1 vertically.

4, 16, 36, 81, 169, 361, 784, 1681, 3600, 7744, 16641, 35721, 76729, 164836, 354025, 760384, 1633284, 3508129, 7535025, 16184529, 34762816, 74666881, 160376896, 344473600, 739894401, 1589218225, 3413480625, 7331811876, 15747991081

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>7

G.f: 4*x -x^2*(-16-20*x-29*x^2-4*x^3+13*x^4+9*x^5) / ( (x^3+2*x^2+x-1)*(x^3-x^2-1) ). - R. J. Mathar, Aug 10 2017

Empirical: 31*a(n) = 114*A002478(n) +133*A002478(n-1) +55*A002478(n) +10*A077961(n) +32*A077961(n-1) -24*A077961(n-2) for n>1. - R. J. Mathar, Nov 09 2018

Example

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

Crossrefs

Row 2 of A207169.

Cf. A002478.

Sequence in context: A085040 A030179 A207025 * A207069 A207436 A189145

Adjacent sequences: A207167 A207168 A207169 * A207171 A207172 A207173

Keyword

nonn

Author

R. H. Hardin, Feb 15 2012

Status

approved