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 A280440 T(n,k)=Number of nXk 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards. 7
 0, 0, 0, 1, 4, 1, 2, 10, 10, 2, 5, 20, 21, 20, 5, 10, 38, 42, 42, 38, 10, 20, 68, 77, 80, 77, 68, 20, 38, 120, 136, 138, 138, 136, 120, 38, 71, 208, 236, 232, 225, 232, 236, 208, 71, 130, 358, 404, 386, 360, 360, 386, 404, 358, 130, 235, 612, 687, 640, 574, 548, 574, 640, 687 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Table starts ...0...0....1....2....5...10...20...38...71..130...235...420...744..1308..2285 ...0...4...10...20...38...68..120..208..358..612..1042..1768..2992..5052..8514 ...1..10...21...42...77..136..236..404..687.1162..1959..3294..5528..9262.15497 ...2..20...42...80..138..232..386..640.1062.1764..2934..4884..8134.13548.22562 ...5..38...77..138..225..360..574..920.1487.2422..3971..6542.10814.17914.29713 ..10..68..136..232..360..548..834.1284.2008.3188..5128..8332.13638.22436.37032 ..20.120..236..386..574..834.1211.1784.2684.4128..6478.10334.16693.27208.44620 ..38.208..404..640..920.1284.1784.2512.3620.5360..8152.12692.20136.32400.52660 ..71.358..687.1062.1487.2008.2684.3620.4989.7078.10365.15642.24224.38290.61451 .130.612.1162.1764.2422.3188.4128.5360.7078.9604.13474.19576.29384.45340.71490 LINKS R. H. Hardin, Table of n, a(n) for n = 1..568 FORMULA Empirical for column k: k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) k=2: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +a(n-4) +a(n-5) k=3: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +a(n-4) +a(n-5) for n>6 k=4: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>7 k=5: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>7 k=6: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>7 k=7: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>7 EXAMPLE Some solutions for n=4 k=4 ..0..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..0. .0..1..0..1 ..0..1..0..1. .1..0..1..1. .1..0..1..0. .1..0..1..0. .0..0..1..0 ..1..0..1..0. .0..1..0..0. .1..1..0..1. .0..1..0..1. .1..1..0..1 ..1..0..1..0. .1..0..1..1. .1..0..1..0. .0..1..0..1. .0..0..1..0 CROSSREFS Column 1 is A001629(n-1). Column 2 is A279262. Sequence in context: A233528 A084604 A152253 * A024569 A206692 A159756 Adjacent sequences:  A280437 A280438 A280439 * A280441 A280442 A280443 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Jan 03 2017 STATUS approved

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Last modified August 1 14:14 EDT 2021. Contains 346391 sequences. (Running on oeis4.)