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A299067 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 4, 1, 2, 18, 18, 2, 3, 64, 141, 64, 3, 5, 236, 993, 993, 236, 5, 8, 888, 7330, 13765, 7330, 888, 8, 13, 3336, 54106, 196699, 196699, 54106, 3336, 13, 21, 12512, 398654, 2827609, 5491159, 2827609, 398654, 12512, 21, 34, 46928, 2937795 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

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

..1.....4.......18.........64...........236..............888...............3336

..1....18......141........993..........7330............54106.............398654

..2....64......993......13765........196699..........2827609...........40585250

..3...236.....7330.....196699.......5491159........154373324.........4331069485

..5...888....54106....2827609.....154373324.......8486867094.......465531179253

..8..3336...398654...40585250....4331069485.....465531179253.....49918355153525

.13.12512..2937795..582407760..121483918174...25530821979245...5351692051251075

.21.46928.21650600.8358259950.3407860943824.1400307860660375.573807870327017333

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) = 4*a(n-1) -2*a(n-2) +4*a(n-3) for n>4

k=3: [order 9] for n>10

k=4: [order 22] for n>23

k=5: [order 62] for n>64

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A231950(n-1).

Sequence in context: A299142 A299373 A299937 * A299728 A299839 A265178

Adjacent sequences:  A299064 A299065 A299066 * A299068 A299069 A299070

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 01 2018

STATUS

approved

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Last modified September 25 18:27 EDT 2022. Contains 356986 sequences. (Running on oeis4.)