A281056 T(n,k)=Number of nXk 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 0, 1, 0, 1, 6, 6, 0, 2, 34, 68, 29, 0, 6, 104, 239, 376, 122, 0, 13, 251, 618, 1022, 1492, 468, 0, 29, 535, 1403, 2452, 3416, 4988, 1686, 0, 60, 1076, 2828, 5400, 7803, 10112, 15028, 5807, 0, 122, 2090, 5482, 10570, 16875, 22106, 27635, 42252, 19338, 0

Offset

1,8

Comments

Table starts

.0.....0......0......1......2.......6......13......29......60......122......241

.0.....1......6.....34....104.....251.....535....1076....2090.....3956.....7353

.0.....6.....68....239....618....1403....2828....5482...10342....19136....34907

.0....29....376...1022...2452....5400...10570...19892...36616....66354...118926

.0...122...1492...3416...7803...16875...32370...59669..107693...191953...339219

.0...468...4988..10112..22106...46610...87995..159317..282552...495655...864369

.0..1686..15028..27635..58005..119205..221212..394884..689397..1191475..2050466

.0..5807..42252..71419.144283..288527..526340..926077.1596265..2721514..4625355

.0.19338.113076.177320.344972..671451.1201939.2084979.3549039..5982952.10051523

.0.62731.291660.426696.800225.1515524.2661939.4546633.7645715.12749511.21211441

Links

R. H. Hardin, Table of n, a(n) for n = 1..338

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = 9*a(n-1) -30*a(n-2) +45*a(n-3) -30*a(n-4) +9*a(n-5) -a(n-6)

k=3: a(n) = 5*a(n-1) -6*a(n-2) -4*a(n-3) +8*a(n-4) for n>6

k=4: [order 12] for n>14

k=5: [order 13] for n>16

k=6: [order 18] for n>21

k=7: [order 19] for n>23

Empirical for row n:

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

n=2: [order 8] for n>14

n=3: [same order 8] for n>15

n=4: [order 9] for n>17

n=5: [same order 9] for n>18

n=6: [same order 9] for n>19

n=7: [same order 9] for n>20

Example

Some solutions for n=4 k=4
..0..0..1..0. .0..0..0..1. .0..1..0..1. .0..1..1..0. .0..1..0..1
..1..1..0..1. .0..1..0..1. .1..0..1..0. .0..1..0..1. .1..0..1..1
..0..1..1..0. .0..1..1..0. .1..0..0..1. .0..1..0..1. .1..0..0..1
..0..0..1..1. .0..1..0..1. .0..1..0..0. .1..0..1..1. .1..0..1..0

Crossrefs

Row 1 is A055243(n-4).

Sequence in context: A364406 A005597 A388212 * A273989 A397194 A197013

Adjacent sequences: A281053 A281054 A281055 * A281057 A281058 A281059

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 13 2017

Status

approved