A305047 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 13, 5, 13, 1, 1, 26, 9, 9, 26, 1, 1, 49, 15, 11, 15, 49, 1, 1, 99, 17, 20, 20, 17, 99, 1, 1, 194, 40, 17, 55, 17, 40, 194, 1, 1, 387, 73, 25, 201, 201, 25, 73, 387, 1, 1, 773, 87, 70, 337, 137, 337, 70, 87, 773, 1, 1, 1538, 219, 67, 1359, 42, 42, 1359

Offset

1,5

Comments

Table starts

.1...1..1..1....1....1....1.......1.......1.......1.........1..........1

.1...4..7.13...26...49...99.....194.....387.....773......1538.......3081

.1...7..5..9...15...17...40......73......87.....219.......433........583

.1..13..9.11...20...17...25......70......67.....101.......292........325

.1..26.15.20...55..201..337....1359....5918...13840.....50917.....214418

.1..49.17.17..201..137...42....5165....6357....5846....188507.....395242

.1..99.40.25..337...42..116....6542....3137....4862....144931.....173351

.1.194.73.70.1359.5165.6542..273937.1450263.3623207..71239378..487361093

.1.387.87.67.5918.6357.3137.1450263.2062731.1912261.381186998.1094057409

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

Formula

Empirical for column k:

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

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

k=3: [order 11] for n>13

k=4: [order 9] for n>13

Example

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

Crossrefs

Column 2 is A304004.

Sequence in context: A081577 A146986 A304141 * A316733 A304010 A305360

Adjacent sequences: A305044 A305045 A305046 * A305048 A305049 A305050

Keyword

nonn,tabl

Author

R. H. Hardin, May 24 2018

Status

approved