A299097 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4, 5 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 7, 4, 8, 13, 13, 8, 16, 29, 20, 29, 16, 32, 73, 41, 41, 73, 32, 64, 157, 101, 125, 101, 157, 64, 128, 353, 242, 574, 574, 242, 353, 128, 256, 869, 578, 1847, 2828, 1847, 578, 869, 256, 512, 1993, 1385, 6007, 9624, 9624, 6007, 1385, 1993, 512, 1024, 4557

Offset

1,2

Comments

Table starts

...1....2....4.....8.....16......32........64........128.........256

...2....7...13....29.....73.....157.......353........869........1993

...4...13...20....41....101.....242.......578.......1385........3368

...8...29...41...125....574....1847......6007......22330.......78424

..16...73..101...574...2828....9624.....44936.....204059......865754

..32..157..242..1847...9624...42012....255009....1414647.....7786685

..64..353..578..6007..44936..255009...2170819...16528508...123272050

.128..869.1385.22330.204059.1414647..16528508..161247816..1570964262

.256.1993.3368.78424.865754.7786685.123272050.1570964262.20536604982

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

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

k=2: a(n) = 4*a(n-1) -5*a(n-2) +10*a(n-3) -24*a(n-4) +16*a(n-5) for n>6

k=3: [order 16] for n>17

k=4: [order 68] for n>69

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A298215.

Sequence in context: A299948 A298221 A299350 * A299879 A299015 A299806

Adjacent sequences: A299094 A299095 A299096 * A299098 A299099 A299100

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 02 2018

Status

approved