A281344 - 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.

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

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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

R. H. Hardin, Table of n, a(n) for n = 1..311

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

Adjacent sequences: A281341 A281342 A281343 * A281345 A281346 A281347

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 20 2017

STATUS

approved