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A305649 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 3, 5, 3, 5, 9, 9, 5, 8, 21, 13, 21, 8, 13, 57, 31, 31, 57, 13, 21, 125, 79, 137, 79, 125, 21, 34, 289, 168, 574, 574, 168, 289, 34, 55, 741, 430, 2360, 5547, 2360, 430, 741, 55, 89, 1737, 1241, 13498, 31079, 31079, 13498, 1241, 1737, 89, 144, 4045, 3577, 83190 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

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

..2....5....9.....21.......57........125..........289............741

..3....9...13.....31.......79........168..........430...........1241

..5...21...31....137......574.......2360........13498..........83190

..8...57...79....574.....5547......31079.......304707........3821570

.13..125..168...2360....31079.....355620......7215825......146459610

.21..289..430..13498...304707....7215825....283691091....10435409852

.34..741.1241..83190..3821570..146459610..10435409852...724085314967

.55.1737.3577.481377.37230262.2640107792.345636487600.42678601156125

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..180

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) +8*a(n-3) -8*a(n-4)

k=3: [order 17] for n>19

k=4: [order 54] for n>57

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A304349.

Sequence in context: A306172 A304355 A305918 * A316925 A305347 A316615

Adjacent sequences:  A305646 A305647 A305648 * A305650 A305651 A305652

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jun 07 2018

STATUS

approved

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Last modified January 24 17:28 EST 2022. Contains 350565 sequences. (Running on oeis4.)