A305097 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4, 6 or 7 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 9, 9, 2, 3, 10, 14, 10, 3, 5, 27, 17, 17, 27, 5, 8, 109, 64, 20, 64, 109, 8, 13, 168, 158, 37, 37, 158, 168, 13, 21, 349, 229, 142, 333, 142, 229, 349, 21, 34, 1229, 630, 295, 1987, 1987, 295, 630, 1229, 34, 55, 2490, 1626, 459, 2220, 7273, 2220, 459

Offset

1,5

Comments

Table starts

..0....1....1....2.....3......5......8......13.......21........34.........55

..1....3....9...10....27....109....168.....349.....1229......2490.......4767

..1....9...14...17....64....158....229.....630.....1626......2950.......6627

..2...10...17...20....37....142....295.....459.....1201......3140.......5679

..3...27...64...37...333...1987...2220....6525....47093....101012.....198933

..5..109..158..142..1987...7273..10652...64966...320192....708423....2636757

..8..168..229..295..2220..10652..23368..101212...548208...1755533....6005884

.13..349..630..459..6525..64966.101212..566292..6089154..19700744...69543035

.21.1229.1626.1201.47093.320192.548208.6089154.64803044.208417821.1176560812

Links

R. H. Hardin, Table of n, a(n) for n = 1..241

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +a(n-2) +8*a(n-3) -16*a(n-5) for n>6

k=3: [order 16] for n>17

k=4: [order 71] for n>72

Example

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

Crossrefs

Column 1 is A000045(n-1).

Sequence in context: A058142 A058144 A132323 * A316757 A055450 A185835

Adjacent sequences: A305094 A305095 A305096 * A305098 A305099 A305100

Keyword

nonn,tabl

Author

R. H. Hardin, May 25 2018

Status

approved