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A305685 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero. 7
1, 1, 1, 1, 4, 1, 1, 8, 8, 1, 1, 24, 25, 24, 1, 1, 82, 139, 139, 82, 1, 1, 272, 818, 1595, 818, 272, 1, 1, 908, 4869, 17947, 17947, 4869, 908, 1, 1, 3076, 29339, 207116, 383910, 207116, 29339, 3076, 1, 1, 10444, 177688, 2403703, 8417922, 8417922, 2403703 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

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

.1.....4.......8........24..........82............272..............908

.1.....8......25.......139.........818...........4869............29339

.1....24.....139......1595.......17947.........207116..........2403703

.1....82.....818.....17947......383910........8417922........185389115

.1...272....4869....207116.....8417922......351440611......14724197226

.1...908...29339...2403703...185389115....14724197226....1172824606532

.1..3076..177688..27979008..4094434997...618597002816...93679147557172

.1.10444.1078090.325990496.90512430926.26011056462909.7488807032051960

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) = 4*a(n-1) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6

k=3: [order 14] for n>16

k=4: [order 38] for n>40

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 2 is A303882.

Sequence in context: A316244 A305954 A317215 * A317065 A316932 A317703

Adjacent sequences:  A305682 A305683 A305684 * A305686 A305687 A305688

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jun 08 2018

STATUS

approved

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Last modified June 27 19:31 EDT 2022. Contains 354898 sequences. (Running on oeis4.)