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A297733
T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2 or 4 neighboring 1s.
13
1, 1, 1, 1, 2, 1, 1, 8, 3, 1, 1, 15, 17, 4, 1, 1, 32, 34, 39, 6, 1, 1, 61, 92, 93, 151, 9, 1, 1, 145, 223, 362, 502, 385, 13, 1, 1, 297, 700, 1103, 2719, 1443, 1026, 19, 1, 1, 658, 1747, 4795, 11341, 11171, 4676, 3272, 28, 1, 1, 1352, 4931, 15646, 82549, 65215, 53173, 19601
OFFSET
1,5
COMMENTS
Table starts
.1..1....1.....1.......1........1.........1...........1............1
.1..2....8....15......32.......61.......145.........297..........658
.1..3...17....34......92......223.......700........1747.........4931
.1..4...39....93.....362.....1103......4795.......15646........61063
.1..6..151...502....2719....11341.....82549......396787......2346541
.1..9..385..1443...11171....65215....673171.....4414693.....36515720
.1.13.1026..4676...53173...414651...6241242....56834907....675663465
.1.19.3272.19601..304157..3199929..74469526...959915987..16537401517
.1.28.8945.62749.1417699.21221319.718454750.13045679082.322119198752
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +a(n-3)
k=3: a(n) = a(n-1) +a(n-2) +13*a(n-3) -2*a(n-4) +4*a(n-5) -11*a(n-6) -3*a(n-7) -a(n-8)
k=4: [order 19]
k=5: [order 35]
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = 2*a(n-1) +a(n-2) -3*a(n-3) +6*a(n-4) -6*a(n-5)
n=3: [order 9]
n=4: [order 27]
n=5: [order 80]
EXAMPLE
Some solutions for n=6 k=4
..0..0..0..0. .0..1..1..1. .0..0..0..0. .0..0..1..0. .0..0..1..1
..0..0..0..0. .0..0..1..0. .0..0..1..1. .0..1..0..1. .0..0..1..1
..0..0..1..1. .0..1..1..1. .0..1..1..0. .0..0..1..1. .0..0..0..0
..0..0..1..1. .0..0..0..0. .0..0..0..0. .0..1..1..0. .0..0..0..0
..0..1..0..1. .0..0..1..1. .0..1..1..0. .0..0..0..0. .0..0..1..1
..0..0..1..0. .0..0..1..1. .1..1..0..0. .0..0..0..0. .0..1..1..0
CROSSREFS
Column 2 is A000930(n+1).
Sequence in context: A119418 A077058 A053373 * A255812 A249141 A353953
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 04 2018
STATUS
approved