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A318350 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7
1, 2, 2, 3, 3, 3, 5, 4, 4, 5, 8, 7, 6, 7, 8, 13, 11, 13, 13, 11, 13, 21, 18, 21, 14, 21, 18, 21, 34, 30, 41, 29, 29, 41, 30, 34, 55, 49, 71, 55, 62, 55, 71, 49, 55, 89, 81, 130, 106, 136, 136, 106, 130, 81, 89, 144, 134, 237, 220, 279, 345, 279, 220, 237, 134, 144, 233, 221, 439 (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......233.......377

..2..3...4...7...11...18....30.....49.....81.....134.....221......365.......603

..3..4...6..13...21...41....71....130....237.....439.....802.....1483......2734

..5..7..13..14...29...55...106....220....432.....885....1788.....3642......7416

..8.11..21..29...62..136...279....624...1344....2941....6444....14202.....31437

.13.18..41..55..136..345...842...2167...5544...14244...36572....94381....243153

.21.30..71.106..279..842..2429...7451..22996...70762..218768...677035...2090867

.34.49.130.220..624.2167..7451..27666.102454..375150.1393359..5163458..19078931

.55.81.237.432.1344.5544.22996.102454.463096.2057916.9235301.41554051.186399590

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..510

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-6)

k=3: [order 19] for n>25

k=4: [order 37] for n>45

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A317767.

Sequence in context: A301662 A317773 A318082 * A127332 A087826 A131624

Adjacent sequences:  A318347 A318348 A318349 * A318351 A318352 A318353

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Aug 24 2018

STATUS

approved

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Last modified May 21 05:07 EDT 2022. Contains 353887 sequences. (Running on oeis4.)