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

1,1

Comments

Column 2 of A231586

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

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).

Example

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

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

Crossrefs

Sequence in context: A196514 A249629 A131459 * A223115 A296381 A240434

Adjacent sequences: A231578 A231579 A231580 * A231582 A231583 A231584

Keyword

nonn

Author

R. H. Hardin, Nov 11 2013

Status

approved