A304669 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 5 or 6 king-move adjacent elements, with upper left element zero.

1, 2, 2, 3, 5, 3, 5, 9, 9, 5, 8, 21, 13, 21, 8, 13, 53, 30, 30, 53, 13, 21, 105, 66, 93, 66, 105, 21, 34, 237, 123, 249, 249, 123, 237, 34, 55, 577, 252, 544, 832, 544, 252, 577, 55, 89, 1205, 535, 1366, 1926, 1926, 1366, 535, 1205, 89, 144, 2681, 1074, 3399, 5311, 5101

Offset

1,2

Comments

Table starts

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

..2....5....9...21....53....105....237.....577....1205.....2681......6349

..3....9...13...30....66....123....252.....535....1074.....2194......4530

..5...21...30...93...249....544...1366....3399....8219....20292.....49933

..8...53...66..249...832...1926...5311...15604...41101...113581....322499

.13..105..123..544..1926...5101..15421...48922..143214...444335...1400682

.21..237..252.1366..5311..15421..49516..163216..516865..1750074...5929076

.34..577..535.3399.15604..48922.163216..597306.2045830..7480857..28310502

.55.1205.1074.8219.41101.143214.516865.2045830.7738947.31691371.133498110

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +8*a(n-3) -4*a(n-4)

k=3: a(n) = a(n-1) +4*a(n-3) +2*a(n-5) -a(n-7) -2*a(n-9) -2*a(n-11) -a(n-12)

k=4: [order 42] for n>43

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A303963.

Sequence in context: A199512 A303969 A304931 * A306172 A304355 A305918

Adjacent sequences: A304666 A304667 A304668 * A304670 A304671 A304672

Keyword

nonn,tabl

Author

R. H. Hardin, May 16 2018

Status

approved