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A303682 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1 or 3 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 3, 5, 3, 5, 7, 7, 5, 8, 17, 9, 17, 8, 13, 31, 15, 15, 31, 13, 21, 49, 25, 28, 25, 49, 21, 34, 103, 39, 44, 44, 39, 103, 34, 55, 193, 57, 64, 76, 64, 57, 193, 55, 89, 327, 87, 90, 110, 110, 90, 87, 327, 89, 144, 641, 137, 132, 150, 177, 150, 132, 137, 641, 144, 233, 1207 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

..1...2...3...5...8..13..21...34...55...89..144..233..377..610...987..1597

..2...5...7..17..31..49.103..193..327..641.1207.2129.4039.7585.13687.25585

..3...7...9..15..25..39..57...87..137..215..329..503..777.1207..1865..2871

..5..17..15..28..44..64..90..132..204..312..466..688.1024.1540..2318..3472

..8..31..25..44..76.110.150..212..306..458..684.1006.1462.2132..3122..4586

.13..49..39..64.110.177.245..335..467..657..949.1391.2035.2937..4221..6079

.21.103..57..90.150.245.367..509..697..957.1311.1851.2671.3869..5547..7907

.34.193..87.132.212.335.509..774.1086.1478.1984.2674.3730.5314..7588.10760

.55.327.137.204.306.467.697.1086.1684.2354.3144.4174.5578.7696.10808.15232

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..1624

FORMULA

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

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

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

k=4: a(n) = a(n-1) +a(n-4) +a(n-5) for n>8

k=5: a(n) = a(n-1) +a(n-4) +a(n-6) for n>10

k=6: a(n) = a(n-1) +a(n-4) +a(n-7) for n>12

k=7: a(n) = a(n-1) +a(n-4) +a(n-8) for n>14

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1).

Column 3 is A052952(n+4) for n>1.

Sequence in context: A197069 A197450 A240406 * A304133 A303808 A304855

Adjacent sequences:  A303679 A303680 A303681 * A303683 A303684 A303685

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Apr 28 2018

STATUS

approved

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Last modified September 18 04:07 EDT 2021. Contains 347506 sequences. (Running on oeis4.)