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A299393 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 6 or 8 king-move adjacent elements, with upper left element zero. 5
1, 2, 2, 3, 4, 3, 5, 3, 3, 5, 8, 13, 3, 13, 8, 13, 34, 9, 9, 34, 13, 21, 73, 17, 63, 17, 73, 21, 34, 203, 48, 119, 119, 48, 203, 34, 55, 594, 94, 243, 508, 243, 94, 594, 55, 89, 1443, 234, 1086, 934, 934, 1086, 234, 1443, 89, 144, 4013, 589, 2782, 6254, 2483, 6254, 2782, 589 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

..1....2...3....5......8.....13......21.......34........55.........89

..2....4...3...13.....34.....73.....203......594......1443.......4013

..3....3...3....9.....17.....48......94......234.......589.......1333

..5...13...9...63....119....243....1086.....2782......8509......31229

..8...34..17..119....508....934....6254....28963....110704.....623533

.13...73..48..243....934...2483...11240....48286....252027....1266960

.21..203..94.1086...6254..11240..112188...649720...3226442...27461474

.34..594.234.2782..28963..48286..649720..5884463..35846074..446459559

.55.1443.589.8509.110704.252027.3226442.35846074.286590596.3734068803

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..219

FORMULA

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = a(n-1) +3*a(n-2) +8*a(n-3) -4*a(n-4) -16*a(n-5) for n>6

k=3: [order 17] for n>18

k=4: [order 71] for n>72

EXAMPLE

Some solutions for n=5 k=7

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A297901.

Column 3 is A298315.

Column 4 is A298316.

Sequence in context: A297907 A298501 A298320 * A299194 A300030 A232451

Adjacent sequences:  A299390 A299391 A299392 * A299394 A299395 A299396

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 09 2018

STATUS

approved

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Last modified January 24 17:24 EST 2021. Contains 340411 sequences. (Running on oeis4.)