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A317863 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 8
0, 1, 1, 1, 3, 1, 2, 6, 6, 2, 3, 10, 4, 10, 3, 5, 21, 19, 19, 21, 5, 8, 46, 32, 56, 32, 46, 8, 13, 102, 72, 155, 155, 72, 102, 13, 21, 220, 164, 313, 350, 313, 164, 220, 21, 34, 491, 331, 851, 1001, 1001, 851, 331, 491, 34, 55, 1077, 790, 2147, 2616, 3315, 2616, 2147, 790 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

..0...1...1....2.....3.....5......8......13......21.......34........55

..1...3...6...10....21....46....102.....220.....491.....1077......2393

..1...6...4...19....32....72....164.....331.....790.....1700......3879

..2..10..19...56...155...313....851....2147....5513....14288.....37168

..3..21..32..155...350..1001...2616....7926...21882....65134....190018

..5..46..72..313..1001..3315...9045...28091...87900...278545....886735

..8.102.164..851..2616..9045..33238..116271..405766..1489264...5416535

.13.220.331.2147..7926.28091.116271..517734.1946626..8076505..33329441

.21.491.790.5513.21882.87900.405766.1946626.8875636.40432932.186507496

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..264

FORMULA

Empirical for column k:

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

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

k=3: [order 26] for n>32

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Sequence in context: A171072 A102035 A055179 * A318214 A318552 A183289

Adjacent sequences:  A317860 A317861 A317862 * A317864 A317865 A317866

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Aug 09 2018

STATUS

approved

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Last modified May 18 23:58 EDT 2021. Contains 344009 sequences. (Running on oeis4.)