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A304697 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 5 or 6 king-move adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 7, 1, 2, 16, 16, 2, 3, 45, 56, 45, 3, 5, 120, 178, 178, 120, 5, 8, 333, 669, 918, 669, 333, 8, 13, 928, 2615, 4910, 4910, 2615, 928, 13, 21, 2613, 9573, 24408, 37050, 24408, 9573, 2613, 21, 34, 7400, 35581, 124399, 263381, 263381, 124399, 35581, 7400 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

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

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

..1...16.....56.....178......669.......2615........9573.........35581

..2...45....178.....918.....4910......24408......124399........641663

..3..120....669....4910....37050.....263381.....1894297......13791026

..5..333...2615...24408...263381....2753404....27769991.....285425506

..8..928...9573..124399..1894297...27769991...389403912....5581948043

.13.2613..35581..641663.13791026..285425506..5581948043..111681916203

.21.7400.133149.3271834.99838011.2949991545.80739890302.2269676763262

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

k=3: [order 19] for n>21

k=4: [order 69] for n>71

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A304013.

Sequence in context: A305367 A304959 A316641 * A316448 A316130 A317436

Adjacent sequences:  A304694 A304695 A304696 * A304698 A304699 A304700

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, May 17 2018

STATUS

approved

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Last modified September 24 03:23 EDT 2021. Contains 347623 sequences. (Running on oeis4.)