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A300689
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
7
0, 1, 1, 1, 3, 1, 2, 10, 10, 2, 3, 30, 53, 30, 3, 5, 96, 272, 272, 96, 5, 8, 307, 1391, 2229, 1391, 307, 8, 13, 981, 7187, 18225, 18225, 7187, 981, 13, 21, 3137, 37100, 150558, 240463, 150558, 37100, 3137, 21, 34, 10034, 191529, 1242620, 3179333, 3179333
OFFSET
1,5
COMMENTS
Table starts
..0.....1......1........2..........3............5..............8
..1.....3.....10.......30.........96..........307............981
..1....10.....53......272.......1391.........7187..........37100
..2....30....272.....2229......18225.......150558........1242620
..3....96...1391....18225.....240463......3179333.......42006289
..5...307...7187...150558....3179333.....67479838.....1431755828
..8...981..37100..1242620...42006289...1431755828....48809162176
.13..3137.191529.10252421..554837022..30366081812..1662541314220
.21.10034.988754.84598340.7328971275.643942334598.56619912876077
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 3*a(n-1) +a(n-2) -3*a(n-4) -2*a(n-5) -a(n-6) for n>7
k=3: [order 14] for n>15
k=4: [order 47] for n>49
EXAMPLE
Some solutions for n=5 k=4
..0..1..1..1. .0..0..1..1. .0..1..0..0. .0..1..1..0. .0..0..0..1
..0..0..0..1. .1..0..1..1. .0..1..1..1. .0..0..0..1. .0..1..0..1
..1..0..1..1. .1..0..0..0. .1..0..1..0. .1..1..1..0. .1..1..0..1
..1..0..0..1. .1..0..1..1. .0..1..0..0. .1..0..1..0. .0..0..0..0
..1..0..1..1. .1..0..0..1. .1..1..1..1. .0..0..1..0. .1..1..1..1
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A300421.
Sequence in context: A185835 A301669 A300427 * A300612 A301354 A229187
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 11 2018
STATUS
approved