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A296804 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1, 3 or 4 king-move neighboring 1s. 8
1, 2, 2, 3, 8, 3, 4, 15, 15, 4, 6, 41, 47, 41, 6, 9, 122, 164, 164, 122, 9, 13, 308, 694, 1011, 694, 308, 13, 19, 855, 2605, 6747, 6747, 2605, 855, 19, 28, 2405, 10149, 40956, 77705, 40956, 10149, 2405, 28, 41, 6522, 40768, 261107, 754400, 754400, 261107, 40768 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

..1....2......3........4.........6...........9............13..............19

..2....8.....15.......41.......122.........308...........855............2405

..3...15.....47......164.......694........2605.........10149...........40768

..4...41....164.....1011......6747.......40956........261107.........1679397

..6..122....694.....6747.....77705......754400.......7978323........85842977

..9..308...2605....40956....754400....11910888.....203660310......3537017110

.13..855..10149...261107...7978323...203660310....5712715858....163079979478

.19.2405..40768..1679397..85842977..3537017110..163079979478...7684218661876

.28.6522.159911.10713116.905014451.60565369990.4582023008983.355189064928041

LINKS

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

FORMULA

Empirical for column k:

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

k=2: a(n) = a(n-1) +3*a(n-2) +9*a(n-3) -4*a(n-4) -12*a(n-5) -16*a(n-6)

k=3: [order 16]

k=4: [order 39]

EXAMPLE

Some solutions for n=5 k=4

..1..0..0..0. .1..1..0..1. .1..0..0..0. .0..1..0..0. .1..0..0..1

..1..0..0..1. .1..1..0..1. .1..0..0..0. .0..0..1..0. .1..0..1..0

..0..0..0..1. .0..0..0..0. .1..1..0..1. .0..0..0..0. .0..0..0..0

..0..0..0..0. .1..1..1..0. .0..1..1..0. .0..0..0..0. .1..1..1..1

..1..1..0..0. .1..1..0..1. .1..0..0..0. .0..1..1..0. .0..0..1..1

CROSSREFS

Column 1 is A000930(n+1).

Sequence in context: A153216 A327259 A295943 * A296952 A141611 A234357

Adjacent sequences:  A296801 A296802 A296803 * A296805 A296806 A296807

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Dec 20 2017

STATUS

approved

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Last modified June 25 18:38 EDT 2022. Contains 354851 sequences. (Running on oeis4.)