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A298280 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 4, 1, 2, 18, 18, 2, 3, 64, 129, 64, 3, 5, 236, 873, 873, 236, 5, 8, 888, 6013, 10679, 6013, 888, 8, 13, 3336, 41437, 136006, 136006, 41437, 3336, 13, 21, 12512, 285280, 1735247, 3214459, 1735247, 285280, 12512, 21, 34, 46928, 1964290 (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......129........873..........6013...........41437............285280

..2....64......873......10679........136006.........1735247..........22110710

..3...236.....6013.....136006.......3214459........75989207........1794078025

..5...888....41437....1735247......75989207......3328434344......145597697355

..8..3336...285280...22110710....1794078025....145597697355....11799327975543

.13.12512..1964290..281745241...42359577845...6369396379414...956310372633436

.21.46928.13524686.3590209542.1000164240246.278645510729761.77508769959888329

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

k=3: [order 10] for n>11

k=4: [order 30] for n>32

k=5: [order 92] for n>96

EXAMPLE

Some solutions for n=4 k=4

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A231950(n-1).

Sequence in context: A299567 A299465 A300108 * A299142 A299373 A299937

Adjacent sequences: A298277 A298278 A298279 * A298281 A298282 A298283

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 16 2018

STATUS

approved

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Last modified December 8 01:51 EST 2022. Contains 358672 sequences. (Running on oeis4.)