A298635 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 6 or 7 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, 25, 25, 14, 94, 1, 1, 173, 21, 45, 34, 45, 21, 173, 1, 1, 340, 41, 81, 61, 61, 81, 41, 340, 1, 1, 601, 70, 186, 107, 163, 107, 186, 70, 601, 1, 1, 1178, 129, 382, 234, 246, 246, 234

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..25...45...81..186..382...832..1778..3817...8229..17739...38337

.1..24..7..25..34...61..107..234..433...961..2031..4286...9049..19572...42207

.1..53.14..45..61..163..246..566.1334..2879..6223.14320..33446..76557..175161

.1..94.21..81.107..246..462..991.1953..4272..9838.22598..52716.122648..291782

.1.173.41.186.234..566..991.2134.4366..9639.22287.50362.114429.263499..617118

.1.340.70.382.433.1334.1953.4366.7520.18205.39703.92437.205166.484401.1134968

Links

R. H. Hardin, Table of n, a(n) for n = 1..419

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 23] for n>29

k=5: [order 58] for n>64

Example

Some solutions for n=5 k=4
..0..0..0..0. .0..1..0..0. .0..0..0..0. .0..0..1..1. .0..0..1..0
..0..1..1..0. .1..1..1..0. .0..1..1..0. .0..1..0..1. .1..0..0..0
..0..1..0..1. .0..0..0..1. .1..0..0..1. .1..1..0..0. .0..0..0..1
..1..0..0..1. .1..0..1..1. .0..1..1..0. .0..0..1..1. .1..0..0..0
..1..1..1..1. .0..0..0..1. .0..0..0..0. .1..0..1..0. .0..0..1..0

Crossrefs

Column 2 is A297980.

Column 3 is A297981.

Sequence in context: A173119 A050178 A297986 * A171146 A174038 A328098

Adjacent sequences: A298632 A298633 A298634 * A298636 A298637 A298638

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 23 2018

Status

approved