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A318545 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7
1, 2, 2, 3, 1, 3, 5, 3, 3, 5, 8, 5, 6, 5, 8, 13, 8, 13, 13, 8, 13, 21, 15, 26, 31, 26, 15, 21, 34, 26, 52, 78, 78, 52, 26, 34, 55, 45, 107, 207, 247, 207, 107, 45, 55, 89, 80, 218, 516, 784, 784, 516, 218, 80, 89, 144, 140, 442, 1288, 2349, 2905, 2349, 1288, 442, 140, 144, 233 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

..1..2...3....5.....8.....13.....21......34.......55........89........144

..2..1...3....5.....8.....15.....26......45.......80.......140........245

..3..3...6...13....26.....52....107.....218......442.......899.......1829

..5..5..13...31....78....207....516....1288.....3270......8271......20866

..8..8..26...78...247....784...2349....7191....22268.....68384.....210050

.13.15..52..207...784...2905..10496...38721...144148....531780....1960675

.21.26.107..516..2349..10496..46165..208159...942764...4213744...18870716

.34.45.218.1288..7191..38721.208159.1143583..6263377..33963639..184912113

.55.80.442.3270.22268.144148.942764.6263377.41368803.271753441.1792754281

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..924

FORMULA

Empirical for column k:

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

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

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

k=4: [order 13] for n>14

k=5: [order 23] for n>24

k=6: [order 37] for n>38

k=7: [order 63] for n>64

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A193147.

Sequence in context: A303719 A299595 A304270 * A071450 A175457 A322025

Adjacent sequences:  A318542 A318543 A318544 * A318546 A318547 A318548

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Aug 28 2018

STATUS

approved

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Last modified January 23 14:34 EST 2022. Contains 350512 sequences. (Running on oeis4.)