login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A281344
T(n,k)=Number of nXk 0..1 arrays with no element equal to more than three of its king-move neighbors and with new values introduced in order 0 sequentially upwards.
8
1, 2, 2, 4, 8, 4, 8, 25, 25, 8, 16, 85, 68, 85, 16, 32, 286, 193, 193, 286, 32, 64, 969, 544, 607, 544, 969, 64, 128, 3281, 1539, 1892, 1892, 1539, 3281, 128, 256, 11114, 4355, 5868, 6256, 5868, 4355, 11114, 256, 512, 37649, 12332, 18189, 19700, 19700, 18189
OFFSET
1,2
COMMENTS
Table starts
...1......2.....4......8......16......32.......64......128.......256.......512
...2......8....25.....85.....286.....969.....3281....11114.....37649....127541
...4.....25....68....193.....544....1539.....4355....12332.....34907.....98797
...8.....85...193....607....1892....5868....18189....56154....173062....534110
..16....286...544...1892....6256...19700....60540...185696....569832...1754082
..32....969..1539...5868...19700...63168...198619...620828...1944159...6105081
..64...3281..4355..18189...60540..198619...639142..2039214...6489813..20683647
.128..11114.12332..56154..185696..620828..2039214..6658147..21625033..70229690
.256..37649.34907.173062..569832.1944159..6489813.21625033..71489598.235986575
.512.127541.98797.534110.1754082.6105081.20683647.70229690.235986575.791069059
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5)
k=3: [order 9] for n>10
k=4: [order 18] for n>21
k=5: [order 49] for n>55
k=6: [order 98] for n>107
EXAMPLE
Some solutions for n=4 k=4
..0..1..0..0. .0..0..1..1. .0..0..0..1. .0..0..0..0. .0..1..1..1
..0..1..0..1. .0..1..0..1. .0..1..1..0. .0..1..1..1. .0..1..0..0
..1..1..0..1. .0..1..0..0. .1..0..0..1. .1..0..0..0. .0..1..0..1
..0..0..0..1. .1..0..1..1. .1..1..1..0. .1..0..1..1. .0..1..0..1
CROSSREFS
Column 1 is A000079(n-1).
Sequence in context: A038208 A240484 A240636 * A298287 A299359 A299180
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 20 2017
STATUS
approved