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A231581 Number of nX2 0..3 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors 1
4, 28, 124, 602, 2776, 12922, 60720, 286047, 1335296, 6256326, 29377828, 137595239, 644951590, 3024402309, 14175895645, 66459189937, 311583082104, 1460702584712, 6848241858778, 32106603868468, 150524267596760, 705711781367756 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 12 19:26 EDT 2020. Contains 335668 sequences. (Running on oeis4.)