A299595 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 3, 1, 3, 5, 3, 3, 5, 8, 5, 5, 5, 8, 13, 8, 11, 11, 8, 13, 21, 15, 19, 23, 19, 15, 21, 34, 26, 35, 53, 53, 35, 26, 34, 55, 45, 65, 121, 113, 121, 65, 45, 55, 89, 80, 120, 250, 256, 256, 250, 120, 80, 89, 144, 140, 220, 533, 541, 576, 541, 533, 220, 140, 144, 233, 245

Offset: 1

Author

R. H. Hardin, Feb 13 2018

Keywords

• nonn
• tabl

Comments

Table starts

..1..2...3....5....8...13....21....34....55.....89....144....233.....377

..2..1...3....5....8...15....26....45....80....140....245....431.....756

..3..3...5...11...19...35....65...120...220....404....744...1369....2517

..5..5..11...23...53..121...250...533..1162...2490...5327..11465...24641

..8..8..19...53..113..256...541..1148..2488...5349..11453..24617...52916

.13.15..35..121..256..576..1225..2601..5625..12100..25921..55696..119716

.21.26..65..250..541.1225..2583..5488.11899..25570..54750.117697..252985

.34.45.120..533.1148.2601..5488.11656.25269..54309.116285.249968..537305

.55.80.220.1162.2488.5625.11899.25269.54738.117679.252010.541648.1164265

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..9934

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A193147.

Formula

Empirical for diagonal: [linear recurrence of order 15] for n>18

Empirical for column k:

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

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

k=3: a(n) = a(n-1) +2*a(n-3) +a(n-4) +a(n-5) for n>8

k=4..99: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>9