A297986 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 6 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 5, 1, 1, 6, 6, 1, 1, 17, 2, 17, 1, 1, 24, 5, 5, 24, 1, 1, 53, 7, 15, 7, 53, 1, 1, 94, 14, 23, 23, 14, 94, 1, 1, 173, 21, 43, 34, 43, 21, 173, 1, 1, 340, 41, 79, 61, 61, 79, 41, 340, 1, 1, 601, 70, 184, 105, 131, 105, 184, 70, 601, 1, 1, 1178, 129, 380, 222, 242, 242, 222

Offset

1,5

Comments

Table starts

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

.1...5..6..17..24...53...94..173..340...601..1178..2137...4056...7565..14086

.1...6..2...5...7...14...21...41...70...129...233...428....783...1445...2664

.1..17..5..15..23...43...79..184..380...830..1776..3815...8227..17737..38335

.1..24..7..23..34...61..105..222..428...948..1975..4162...8801..18972..40777

.1..53.14..43..61..131..242..530.1226..2701..5847.13187..30316..68963.156767

.1..94.21..79.105..242..444..935.1835..3921..8793.19694..44948.102048.235955

.1.173.41.184.222..530..935.1980.3832..8355.18941.40962..89009.197337.448014

.1.340.70.380.428.1226.1835.3832.6500.15690.33619.75185.159728.361567.821919

Links

R. H. Hardin, Table of n, a(n) for n = 1..511

Formula

Empirical for column k:

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

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

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

k=4: [order 22] for n>28

k=5: [order 37] for n>43

k=6: [order 76] for n>84

Example

Some solutions for n=7 k=4
..0..0..1..1. .0..0..1..0. .0..0..1..0. .0..1..1..1. .0..0..0..0
..0..1..0..1. .0..1..1..1. .0..1..1..1. .0..0..1..0. .0..1..1..0
..1..0..1..0. .1..0..0..0. .1..0..0..0. .0..1..1..1. .1..0..1..0
..1..0..1..0. .0..1..1..0. .0..1..1..0. .1..0..0..0. .1..0..1..0
..1..0..1..0. .0..1..0..1. .0..0..1..0. .0..1..1..0. .1..0..1..0
..1..0..0..1. .1..0..0..1. .1..0..1..0. .0..1..0..1. .0..1..0..1
..1..1..1..1. .1..1..1..1. .1..1..0..0. .0..0..1..1. .0..0..1..1

Crossrefs

Sequence in context: A028313 A173119 A050178 * A298635 A171146 A174038

Adjacent sequences: A297983 A297984 A297985 * A297987 A297988 A297989

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 10 2018

Status

approved