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A302670
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
10
0, 1, 0, 1, 3, 0, 2, 14, 11, 0, 3, 45, 43, 34, 0, 5, 146, 164, 194, 111, 0, 8, 537, 760, 934, 691, 361, 0, 13, 1934, 3425, 6110, 4267, 2802, 1172, 0, 21, 6861, 15569, 38736, 42367, 21949, 10660, 3809, 0, 34, 24386, 70323, 251254, 352174, 316977, 106793, 41839
OFFSET
1,5
COMMENTS
Table starts
.0.....1......1.......2.........3..........5............8............13
.0.....3.....14......45.......146........537.........1934..........6861
.0....11.....43.....164.......760.......3425........15569.........70323
.0....34....194.....934......6110......38736.......251254.......1610569
.0...111....691....4267.....42367.....352174......3204956......28324200
.0...361...2802...21949....316977....3640304.....46360666.....582115385
.0..1172..10660..106793...2320879...35549458....637088915...11181864782
.0..3809..41839..529984..17037458..353912413...8880747825..219692176894
.0.12377.161878.2617548.125456575.3503182605.123521424862.4291098950499
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
k=3: [order 14]
k=4: [order 32] for n>35
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) +3*a(n-2) +6*a(n-3) +10*a(n-4) +4*a(n-5) for n>6
n=3: [order 15] for n>17
n=4: [order 54] for n>58
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..1. .0..0..1..1. .0..1..1..0. .0..1..1..1. .0..1..1..0
..1..1..0..1. .0..1..0..0. .1..0..0..1. .0..0..1..1. .1..0..0..1
..1..1..0..1. .1..0..1..1. .1..1..0..0. .1..0..0..0. .1..0..0..1
..0..0..1..0. .0..0..1..0. .0..1..0..1. .0..1..1..1. .1..1..1..1
..0..0..1..1. .1..1..0..1. .1..0..1..1. .1..0..0..1. .0..0..0..0
CROSSREFS
Column 2 is A180762.
Row 1 is A000045(n-1).
Row 2 is A302225.
Row 3 is A302226.
Row 4 is A302227.
Sequence in context: A239098 A319501 A302224 * A302472 A303254 A256068
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 11 2018
STATUS
approved