A300350 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1 or 2 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 1, 1, 1, 2, 1, 2, 6, 6, 2, 3, 15, 9, 15, 3, 5, 37, 26, 26, 37, 5, 8, 90, 57, 58, 57, 90, 8, 13, 223, 133, 152, 152, 133, 223, 13, 21, 550, 306, 325, 306, 325, 306, 550, 21, 34, 1355, 709, 729, 729, 729, 729, 709, 1355, 34, 55, 3341, 1642, 1609, 1496, 1371, 1496, 1609

Offset

1,5

Comments

Table starts

..0....1....1....2....3.....5.....8....13....21.....34.....55.....89.....144

..1....2....6...15...37....90...223...550..1355...3341...8237..20307...50064

..1....6....9...26...57...133...306...709..1642...3805...8811..20409...47276

..2...15...26...58..152...325...729..1609..3577...7931..17605..39106...86859

..3...37...57..152..306...729..1496..3223..6893..14847..31957..68842..148439

..5...90..133..325..729..1371..3092..6068.12638..26306..55227.116124..244628

..8..223..306..729.1496..3092..5451.12038.22852..46541..95132.196177..405629

.13..550..709.1609.3223..6068.12038.20316.44961..83436.167732.339040..690762

.21.1355.1642.3577.6893.12638.22852.44961.73826.165976.303634.606479.1218187

Links

R. H. Hardin, Table of n, a(n) for n = 1..682

Formula

Empirical for column k:

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

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

k=3: a(n) = 2*a(n-1) +a(n-2) -2*a(n-5) -2*a(n-6) -2*a(n-7) -a(n-8) for n>10

k=4: [order 13] for n>16

k=5: [order 15] for n>19

k=6: [order 17] for n>22

k=7: [order 19] for n>25

Example

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

Crossrefs

Column 1 is A000045(n-1).

Sequence in context: A286651 A324342 A140835 * A300435 A300769 A300639

Adjacent sequences: A300347 A300348 A300349 * A300351 A300352 A300353

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 03 2018

Status

approved