A221448 Number of 3 X n binary arrays with every 0 a horizontal or antidiagonal neighbor to some 1.

1, 31, 221, 1465, 10593, 76055, 543081, 3883061, 27769277, 198564543, 1419847869, 10152784401, 72598518713, 519122981715, 3712041493221, 26543328598837, 189800757263741, 1357189525524527, 9704721072833461, 69394590298217165, 496213041736290005, 3548221579435255963

Offset

1,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (5,8,46,39,69,-10,-38,-68,-40,50,18,-13,-7,4,2,-1,1).

Formula

Empirical: a(n) = 5*a(n-1) +8*a(n-2) +46*a(n-3) +39*a(n-4) +69*a(n-5) -10*a(n-6) -38*a(n-7) -68*a(n-8) -40*a(n-9) +50*a(n-10) +18*a(n-11) -13*a(n-12) -7*a(n-13) +4*a(n-14) +2*a(n-15) -a(n-16) +a(n-17).

The above empirical formula confirmed using the transfer matrix method. - Andrew Howroyd, Jul 18 2026

Example

Some solutions for n=3:
..0..1..1....1..1..0....1..1..1....1..1..1....0..1..0....0..1..1....1..0..1
..1..1..0....0..1..1....1..1..1....0..1..1....0..0..1....0..1..1....1..1..1
..1..0..1....1..1..1....0..1..0....1..1..1....1..1..1....1..0..1....1..1..0

Crossrefs

Row 3 of A221446.

Sequence in context: A183792 A183784 A042874 * A001136 A256172 A142939

Adjacent sequences: A221445 A221446 A221447 * A221449 A221450 A221451

Keyword

nonn,easy,changed

Author

R. H. Hardin, Jan 17 2013

Extensions

New name from Andrew Howroyd, Jul 18 2026

Status

approved