A305489 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 6 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 7, 1, 2, 14, 14, 2, 3, 33, 19, 33, 3, 5, 70, 27, 27, 70, 5, 8, 157, 137, 65, 137, 157, 8, 13, 346, 295, 195, 195, 295, 346, 13, 21, 769, 570, 125, 2094, 125, 570, 769, 21, 34, 1710, 2026, 268, 7007, 7007, 268, 2026, 1710, 34, 55, 3813, 4727, 1176, 16464, 23229

Offset

1,5

Comments

Table starts

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

..1....7...14...33.....70.....157.....346.......769.......1710........3813

..1...14...19...27....137.....295.....570......2026.......4727.......10623

..2...33...27...65....195.....125.....268......1176........805........1681

..3...70..137..195...2094....7007...16464.....91350.....348956.....1047508

..5..157..295..125...7007...23229...52124....581383....2463954.....8570618

..8..346..570..268..16464...52124...65452...2034173....7974852....20131094

.13..769.2026.1176..91350..581383.2034173..35294211..261130745..1568168588

.21.1710.4727..805.348956.2463954.7974852.261130745.2468446765.16736271764

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) = 2*a(n-1) +3*a(n-2) -2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6

k=3: [order 14] for n>16

k=4: [order 17] for n>22

k=5: [order 97] for n>100

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A304143.

Sequence in context: A273984 A119506 A304149 * A305089 A316740 A304019

Adjacent sequences: A305486 A305487 A305488 * A305490 A305491 A305492

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 02 2018

Status

approved