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A316583
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 7 or 8 king-move adjacent elements, with upper left element zero.
7
0, 1, 1, 1, 7, 1, 2, 23, 23, 2, 3, 86, 63, 86, 3, 5, 313, 338, 338, 313, 5, 8, 1145, 1312, 2477, 1312, 1145, 8, 13, 4184, 5936, 15200, 15200, 5936, 4184, 13, 21, 15293, 25271, 98828, 130212, 98828, 25271, 15293, 21, 34, 55895, 110555, 634867, 1216428, 1216428
OFFSET
1,5
COMMENTS
Table starts
..0.....1......1........2.........3...........5.............8.............13
..1.....7.....23.......86.......313........1145..........4184..........15293
..1....23.....63......338......1312........5936.........25271.........110555
..2....86....338.....2477.....15200.......98828........634867........4075278
..3...313...1312....15200....130212.....1216428......11450072......105422515
..5..1145...5936....98828...1216428....15492767.....209344758.....2702476568
..8..4184..25271...634867..11450072...209344758....4227286531....79708721021
.13.15293.110555..4075278.105422515..2702476568...79708721021..2151886485463
.21.55895.478290.26237510.988545949.35886237100.1560689236544.60957630655386
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) +4*a(n-3) +4*a(n-4)
k=3: [order 15] for n>16
k=4: [order 46] for n>48
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..0. .0..0..1..0. .0..1..0..1. .0..1..1..0. .0..0..0..0
..1..0..0..1. .0..1..0..1. .0..0..1..1. .1..0..1..0. .1..0..1..0
..0..0..0..1. .0..0..0..0. .1..1..0..0. .1..1..1..1. .1..1..0..0
..0..1..0..0. .0..1..0..1. .1..1..0..0. .0..0..0..1. .1..0..0..1
..0..0..0..1. .0..0..1..1. .1..0..0..1. .1..0..0..0. .0..0..1..0
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A303890.
Sequence in context: A303896 A305288 A304901 * A304597 A316383 A306143
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 07 2018
STATUS
approved