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A316311 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 6 or 8 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 3, 5, 3, 5, 7, 7, 5, 8, 17, 10, 17, 8, 13, 35, 21, 21, 35, 13, 21, 61, 44, 74, 44, 61, 21, 34, 127, 83, 148, 148, 83, 127, 34, 55, 265, 168, 404, 662, 404, 168, 265, 55, 89, 507, 365, 1046, 1488, 1488, 1046, 365, 507, 89, 144, 1013, 766, 3023, 4583, 4431, 4583 (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.........144

..2...5...7...17....35.....61.....127......265.......507.......1013........2071

..3...7..10...21....44.....83.....168......365.......766.......1615........3490

..5..17..21...74...148....404....1046.....3023......8295......24149.......72052

..8..35..44..148...662...1488....4583....18558.....56204.....188141......712440

.13..61..83..404..1488...4431...17487....75221....293206....1262596.....5656690

.21.127.168.1046..4583..17487...96175...534083...2689151...15357780....89959730

.34.265.365.3023.18558..75221..534083..3854852..23640130..172324121..1280488352

.55.507.766.8295.56204.293206.2689151.23640130.190235425.1767871577.16603983388

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) = 2*a(n-1) -a(n-2) +4*a(n-3) -4*a(n-4) for n>5

k=3: [order 16]

k=4: [order 67] for n>68

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A303802.

Sequence in context: A305482 A305252 A316552 * A317266 A067330 A202874

Adjacent sequences:  A316308 A316309 A316310 * A316312 A316313 A316314

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jun 29 2018

STATUS

approved

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Last modified April 20 17:54 EDT 2019. Contains 322310 sequences. (Running on oeis4.)