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A305367 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 7, 1, 2, 16, 16, 2, 3, 45, 39, 45, 3, 5, 120, 107, 107, 120, 5, 8, 333, 310, 398, 310, 333, 8, 13, 928, 943, 1532, 1532, 943, 928, 13, 21, 2613, 2935, 5465, 7196, 5465, 2935, 2613, 21, 34, 7400, 9077, 21691, 32765, 32765, 21691, 9077, 7400, 34, 55, 21053 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

..0....1.....1......2.......3........5.........8.........13..........21

..1....7....16.....45.....120......333.......928.......2613........7400

..1...16....39....107.....310......943......2935.......9077.......28054

..2...45...107....398....1532.....5465.....21691......82625......320130

..3..120...310...1532....7196....32765....163682.....791180.....3881007

..5..333...943...5465...32765...179644...1113793....6595796....39677540

..8..928..2935..21691..163682..1113793...8803975...65762626...500606134

.13.2613..9077..82625..791180..6595796..65762626..615439372..5858512208

.21.7400.28054.320130.3881007.39677540.500606134.5858512208.69977566829

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..199

FORMULA

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +5*a(n-2) -2*a(n-3) -12*a(n-4) -8*a(n-5) for n>6

k=3: [order 18]

k=4: [order 66] for n>68

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A304013.

Sequence in context: A305089 A316740 A304019 * A304959 A316641 A304697

Adjacent sequences:  A305364 A305365 A305366 * A305368 A305369 A305370

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, May 31 2018

STATUS

approved

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Last modified October 27 12:08 EDT 2021. Contains 348276 sequences. (Running on oeis4.)