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A231515 T(n,k)=Number of nXk 0..1 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors 8
2, 2, 2, 4, 6, 4, 7, 14, 14, 7, 12, 35, 78, 35, 12, 21, 90, 343, 343, 90, 21, 37, 225, 1537, 2594, 1537, 225, 37, 65, 569, 7505, 19435, 19435, 7505, 569, 65, 114, 1441, 35872, 158061, 256846, 158061, 35872, 1441, 114, 200, 3640, 168887, 1275558, 3691558 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

...2....2.......4.........7...........12.............21...............37

...2....6......14........35...........90............225..............569

...4...14......78.......343.........1537...........7505............35872

...7...35.....343......2594........19435.........158061..........1275558

..12...90....1537.....19435.......256846........3691558.........51741521

..21..225....7505....158061......3691558.......97188562.......2438335793

..37..569...35872...1275558.....51741521.....2438335793.....108221463798

..65.1441..168887..10130742....714951561....59978232085....4680280632866

.114.3640..800573..80645991...9949033842..1495872774439..205954365382497

.200.9208.3806573.644138583.138737920339.37400468849958.9095707696345723

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..220

FORMULA

Empirical for column k:

k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3) for n>4

k=2: a(n) = 2*a(n-1) +a(n-2) +3*a(n-3) -4*a(n-4) -2*a(n-5) -4*a(n-6)

k=3: [order 16] for n>17

k=4: [order 34] for n>35

EXAMPLE

Some solutions for n=4 k=4

..1..1..1..0....1..0..0..0....0..0..1..0....1..0..0..0....0..0..0..1

..1..1..0..0....1..0..0..1....0..0..0..0....0..0..0..0....1..0..0..1

..0..0..0..1....0..0..1..1....1..0..1..0....1..0..0..0....1..0..0..0

..0..0..0..0....0..0..1..1....0..0..0..0....1..1..0..0....1..1..0..1

CROSSREFS

Column 1 is A005251(n+2)

Sequence in context: A342271 A240433 A217637 * A231544 A086420 A328106

Adjacent sequences:  A231512 A231513 A231514 * A231516 A231517 A231518

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Nov 09 2013

STATUS

approved

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Last modified September 20 08:10 EDT 2021. Contains 347577 sequences. (Running on oeis4.)