A297923 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 4 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 4, 1, 2, 17, 17, 2, 3, 61, 109, 61, 3, 5, 216, 588, 588, 216, 5, 8, 793, 3276, 4771, 3276, 793, 8, 13, 2907, 18451, 41762, 41762, 18451, 2907, 13, 21, 10622, 103558, 366976, 575754, 366976, 103558, 10622, 21, 34, 38809, 581318, 3211086, 7960069

Offset

1,5

Comments

Table starts

..0.....1.......1.........2...........3.............5...............8

..1.....4......17........61.........216...........793............2907

..1....17.....109.......588........3276.........18451..........103558

..2....61.....588......4771.......41762........366976.........3211086

..3...216....3276.....41762......575754.......7960069.......109611795

..5...793...18451....366976.....7960069.....173216147......3751364813

..8..2907..103558...3211086...109611795....3751364813....127727388127

.13.10622..581318..28124318..1511726778...81401727872...4359449485941

.21.38809.3263838.246367034.20851649928.1766726336073.148831641978201

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

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

k=3: [order 9] for n>12

k=4: [order 31] for n>34

Example

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

Crossrefs

Column 1 is A000045(n-1).

Sequence in context: A298846 A298653 A299607 * A298547 A298337 A299398

Adjacent sequences: A297920 A297921 A297922 * A297924 A297925 A297926

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 08 2018

Status

approved