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A317160 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 3, 5, 3, 5, 9, 9, 5, 8, 21, 14, 21, 8, 13, 57, 29, 29, 57, 13, 21, 125, 73, 105, 73, 125, 21, 34, 289, 165, 379, 379, 165, 289, 34, 55, 741, 394, 1245, 2345, 1245, 394, 741, 55, 89, 1737, 1068, 5458, 9686, 9686, 5458, 1068, 1737, 89, 144, 4045, 3018, 25315, 65283 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

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

..2....5....9.....21......57.......125........289..........741...........1737

..3....9...14.....29......73.......165........394.........1068...........3018

..5...21...29....105.....379......1245.......5458........25315.........111407

..8...57...73....379....2345......9686......65283.......549872........3771839

.13..125..165...1245....9686.....69701.....887617.....10940249......123485236

.21..289..394...5458...65283....887617...20168266....403588059.....7455221517

.34..741.1068..25315..549872..10940249..403588059..13792577708...402260884943

.55.1737.3018.111407.3771839.123485236.7455221517.402260884943.18922956181705

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 18] for n>20

k=4: [order 66] for n>69

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A304349.

Sequence in context: A316427 A317429 A316239 * A317043 A317697 A132403

Adjacent sequences:  A317157 A317158 A317159 * A317161 A317162 A317163

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jul 22 2018

STATUS

approved

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Last modified October 21 07:28 EDT 2021. Contains 348148 sequences. (Running on oeis4.)