A298187 T(n,k)=Number of nXk 0..1 arrays with every element equal to 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 2, 0, 0, 3, 2, 2, 3, 0, 0, 5, 3, 3, 3, 5, 0, 0, 8, 5, 4, 4, 5, 8, 0, 0, 13, 8, 6, 5, 6, 8, 13, 0, 0, 21, 13, 9, 7, 7, 9, 13, 21, 0, 0, 34, 21, 14, 10, 10, 10, 14, 21, 34, 0, 0, 55, 34, 22, 15, 14, 14, 15, 22, 34, 55, 0, 0, 89, 55, 35, 23, 20, 19, 20, 23, 35, 55

Offset: 1

Author

R. H. Hardin, Jan 14 2018

Keywords

• nonn
• tabl

Comments

Table starts

.0..0..0..0..0..0..0..0..0...0...0...0...0....0....0....0....0.....0.....0

.0..1..1..2..3..5..8.13.21..34..55..89.144..233..377..610..987..1597..2584

.0..1..1..2..3..5..8.13.21..34..55..89.144..233..377..610..987..1597..2584

.0..2..2..3..4..6..9.14.22..35..56..90.145..234..378..611..988..1598..2585

.0..3..3..4..5..7.10.15.23..36..57..91.146..235..379..612..989..1599..2586

.0..5..5..6..7.10.14.20.29..44..68.106.166..262..416..663.1059..1695..2718

.0..8..8..9.10.14.19.27.38..58..90.142.225..362..587..959.1572..2587..4270

.0.13.13.14.15.20.27.41.58..91.145.240.398..680.1157.2003.3476..6073.10620

.0.21.21.22.23.29.38.58.81.127.203.341.574.1019.1784.3212.5779.10480.18971

Examples

			Some solutions for n=7 k=4
..0..0..0..0. .0..0..1..1. .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..0..0. .0..0..1..1. .0..0..0..0. .1..1..1..1. .0..0..0..0
..0..0..0..0. .0..0..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1
..0..0..0..0. .0..0..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1
..0..0..0..0. .0..0..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..760

Crossrefs

Column 2 is A000045(n-1).

Column 3 is A000045(n-1).

Column 4 is A001611(n-1).

Column 5 is A157725(n-1).

Formula

Empirical for column k:

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

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

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

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

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

k=6: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +2*a(n-4) -2*a(n-5) +a(n-7) for n>8

k=7: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +2*a(n-4) -2*a(n-5) +a(n-6) -a(n-7) +a(n-8) -a(n-10) +a(n-11) for n>12