A231581 Number of nX2 0..3 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

4, 28, 124, 602, 2776, 12922, 60720, 286047, 1335296, 6256326, 29377828, 137595239, 644951590, 3024402309, 14175895645, 66459189937, 311583082104, 1460702584712, 6848241858778, 32106603868468, 150524267596760, 705711781367756

Offset: 1

Author

R. H. Hardin, Nov 11 2013

Keywords

• nonn

Comments

Column 2 of A231586

Examples

			Some solutions for n=7
..0..0....3..0....2..1....0..3....2..0....2..3....2..2....1..1....3..3....0..0
..0..2....0..0....1..1....0..0....0..0....2..2....0..0....2..1....0..0....0..1
..1..0....0..0....0..0....0..1....1..0....3..2....0..0....1..2....0..0....0..0
..0..0....0..2....0..0....0..2....0..0....1..1....1..3....0..0....0..3....3..0
..2..0....0..1....0..2....0..0....0..1....1..1....0..0....0..0....0..0....0..1
..2..0....0..0....2..0....0..0....0..0....1..1....0..0....0..0....3..0....0..0
..0..0....0..0....0..0....2..0....3..0....2..1....2..3....0..2....0..0....0..3
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1488 (first 210 terms from R. H. Hardin)
• Robert Israel, Maple-assisted proof of formula

Programs

Maple

rec:= a(n) = 4*a(n-1) +6*a(n-2) +38*a(n-3) -161*a(n-4) -292*a(n-5) -953*a(n-6) +1185*a(n-7) +4928*a(n-8) +12336*a(n-9) +7076*a(n-10) -7076*a(n-11) -24464*a(n-12) -24608*a(n-13) -18624*a(n-14) -6720*a(n-15) -2304*a(n-16):
Data := [4, 28, 124, 602, 2776, 12922, 60720, 286047, 1335296, 6256326, 29377828, 137595239, 644951590, 3024402309, 14175895645, 66459189937]:
f:= gfun:-rectoproc({rec,seq(a(i)=Data[i],i=1..16)},a(n),remember):
map(f, [$1..40]); # Robert Israel, Dec 06 2017

Formula

Empirical: a(n) = 4*a(n-1) +6*a(n-2) +38*a(n-3) -161*a(n-4) -292*a(n-5) -953*a(n-6) +1185*a(n-7) +4928*a(n-8) +12336*a(n-9) +7076*a(n-10) -7076*a(n-11) -24464*a(n-12) -24608*a(n-13) -18624*a(n-14) -6720*a(n-15) -2304*a(n-16).

Empirical formula verified by Robert Israel, Dec 06 2017 (see link).