A300342 - OEIS

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A300342

T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 5, 1, 1, 13, 13, 1, 1, 42, 47, 42, 1, 1, 127, 255, 255, 127, 1, 1, 389, 1272, 2648, 1272, 389, 1, 1, 1192, 6780, 25327, 25327, 6780, 1192, 1, 1, 3645, 36498, 258608, 476507, 258608, 36498, 3645, 1, 1, 11161, 198531, 2697270, 9482056, 9482056

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,5

COMMENTS

Table starts

.1.....1.......1.........1...........1..............1................1

.1.....5......13........42.........127............389.............1192

.1....13......47.......255........1272...........6780............36498

.1....42.....255......2648.......25327.........258608..........2697270

.1...127....1272.....25327......476507........9482056........193080853

.1...389....6780....258608.....9482056......366298010......14485201471

.1..1192...36498...2697270...193080853....14485201471....1111703589144

.1..3645..198531..28350215..3949300187...574690828973...85529683934894

.1.11161.1088200.300252749.81288738492.22936158924074.6617480992614301

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)

k=2: a(n) = a(n-1) +5*a(n-2) +4*a(n-3)

k=3: [order 11] for n>13

k=4: [order 25] for n>26

k=5: [order 66] for n>69

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 2 is A298234.

Sequence in context: A299060 A299821 A299721 * A119725 A239279 A278880

Adjacent sequences: A300339 A300340 A300341 * A300343 A300344 A300345

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Mar 03 2018

STATUS

approved