A202902 Number of nX4 0..1 arrays with every one equal to some NW, E or S neighbor.

1, 40, 494, 4892, 51068, 538672, 5654616, 59369072, 623600944, 6549786560, 68792261728, 722531010240, 7588808329152, 79705877679872, 837157507203456, 8792735883863808, 92350844763980544, 969968692011129856

Offset

1,2

Links

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

Robert Israel, Maple-assisted proof of formula

Formula

Empirical: a(n) = 16*a(n-1) -76*a(n-2) +272*a(n-3) -1060*a(n-4) +2704*a(n-5) -5184*a(n-6) +9920*a(n-7) -11904*a(n-8) +9472*a(n-9) -7168*a(n-10) +4096*a(n-11) -1024*a(n-12).

Empirical formula verified by Robert Israel, May 09 2018 (see link).

Example

Some solutions for n=5
..1..1..1..0....1..0..1..1....0..0..0..0....1..0..0..0....0..1..1..1
..0..1..1..0....1..0..1..1....0..1..1..0....1..1..1..0....1..1..0..1
..0..1..1..1....1..0..1..0....1..0..1..0....1..1..1..0....0..1..1..1
..1..0..1..1....1..1..1..1....1..0..0..0....0..1..0..0....1..1..0..1
..1..1..0..0....0..1..0..0....1..1..0..0....1..1..1..0....0..1..0..0

Maple

f:= gfun:-rectoproc({a(n) = 16*a(n-1) -76*a(n-2) +272*a(n-3) -1060*a(n-4) +2704*a(n-5) -5184*a(n-6) +9920*a(n-7) -11904*a(n-8) +9472*a(n-9) -7168*a(n-10) +4096*a(n-11) -1024*a(n-12), seq(a(i)=[1, 40, 494, 4892, 51068, 538672, 5654616, 59369072, 623600944, 6549786560, 68792261728, 722531010240][i], i=1..12)}, a(n), remember):
map(f, [$1..25]); # Robert Israel, May 09 2018

Crossrefs

Column 4 of A202906.

Sequence in context: A186933 A271650 A177096 * A140045 A223162 A069079

Adjacent sequences: A202899 A202900 A202901 * A202903 A202904 A202905

Keyword

nonn

Author

R. H. Hardin, Dec 25 2011

Status

approved