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A318037 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 8
1, 2, 2, 3, 3, 3, 5, 6, 6, 5, 8, 11, 9, 11, 8, 13, 22, 25, 25, 22, 13, 21, 46, 58, 69, 58, 46, 21, 34, 91, 152, 176, 176, 152, 91, 34, 55, 182, 368, 472, 580, 472, 368, 182, 55, 89, 371, 904, 1222, 1910, 1910, 1222, 904, 371, 89, 144, 746, 2211, 3354, 6525, 7728, 6525 (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

..2...3....6...11....22.....46......91......182........371.........746

..3...6....9...25....58....152.....368......904.......2211........5420

..5..11...25...69...176....472....1222.....3354.......9209.......25092

..8..22...58..176...580...1910....6525....23463......84609......306640

.13..46..152..472..1910...7728...32385...148465.....679005.....3172701

.21..91..368.1222..6525..32385..204645..1284756....8133386....51773454

.34.182..904.3354.23463.148465.1284756.10928383...94939015...818553114

.55.371.2211.9209.84609.679005.8133386.94939015.1157058721.13783060247

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..220

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-3) +a(n-5) -a(n-6)

k=3: [order 30] for n>33

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1).

Sequence in context: A029093 A301541 A240519 * A326165 A078462 A239518

Adjacent sequences:  A318034 A318035 A318036 * A318038 A318039 A318040

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Aug 13 2018

STATUS

approved

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Last modified March 5 16:12 EST 2021. Contains 341825 sequences. (Running on oeis4.)