

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.


14



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
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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(n1)
k=2: a(n) = 9*a(n1) 30*a(n2) +45*a(n3) 30*a(n4) +9*a(n5) a(n6)
k=3: a(n) = 5*a(n1) 6*a(n2) 4*a(n3) +8*a(n4) 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(n1) 5*a(n3) +3*a(n5) +a(n6)
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(n4).
Sequence in context: A283203 A155742 A005597 * A273989 A197013 A329092
Adjacent sequences: A281053 A281054 A281055 * A281057 A281058 A281059


KEYWORD

nonn,tabl


AUTHOR

R. H. Hardin, Jan 13 2017


STATUS

approved



