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A316448 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 7, 1, 2, 16, 16, 2, 3, 45, 57, 45, 3, 5, 120, 182, 182, 120, 5, 8, 333, 712, 946, 712, 333, 8, 13, 928, 2832, 5256, 5256, 2832, 928, 13, 21, 2613, 10696, 26592, 43568, 26592, 10696, 2613, 21, 34, 7400, 41107, 139705, 325839, 325839, 139705, 41107 (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.....57.....182.......712.......2832........10696.........41107

..2...45....182.....946......5256......26592.......139705........743357

..3..120....712....5256.....43568.....325839......2520180......19750414

..5..333...2832...26592....325839....3624515.....39827783.....450251619

..8..928..10696..139705...2520180...39827783....621643922...10080547097

.13.2613..41107..743357..19750414..450251619..10080547097..235652502418

.21.7400.157988.3895564.153125421.5054524591.161747868059.5454074957154

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 20] for n>21

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

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A304013.

Sequence in context: A304959 A316641 A304697 * A316130 A317436 A303896

Adjacent sequences:  A316445 A316446 A316447 * A316449 A316450 A316451

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jul 03 2018

STATUS

approved

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Last modified October 18 21:56 EDT 2021. Contains 348070 sequences. (Running on oeis4.)