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 A240783 T(n,k)=Number of nXk 0..1 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..1 introduced in row major order 12
 1, 1, 2, 1, 3, 4, 1, 4, 11, 8, 1, 6, 20, 34, 16, 1, 9, 46, 97, 111, 32, 1, 14, 97, 305, 459, 361, 64, 1, 22, 216, 959, 2167, 2187, 1172, 128, 1, 35, 472, 3033, 10150, 15332, 10442, 3809, 256, 1, 56, 1043, 9581, 47920, 106411, 108509, 49861, 12377, 512, 1, 90, 2296, 30354 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Table starts ...1.....1.......1........1..........1...........1.............1..............1 ...2.....3.......4........6..........9..........14............22.............35 ...4....11......20.......46.........97.........216...........472...........1043 ...8....34......97......305........959........3033..........9581..........30354 ..16...111.....459.....2167......10150.......47920........226532........1071982 ..32...361....2187....15332.....106411......746346.......5228820.......36701371 ..64..1172...10442...108509....1120383....11677893.....121621207.....1269199948 .128..3809...49861...767834...11791412...182610635....2827515311....43857418181 .256.12377..238068..5434887..124095989..2856212777...65742420202..1515928067679 .512.40218.1136678.38467875.1306056075.44672652785.1528546759636.52397680462958 LINKS R. H. Hardin, Table of n, a(n) for n = 1..264 FORMULA Empirical for column k: k=1: a(n) = 2*a(n-1) k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4) k=3: a(n) = 5*a(n-1) -a(n-2) -a(n-3) +4*a(n-4) -4*a(n-5) -3*a(n-6) +a(n-7) k=4: [order 22] k=5: [order 54] Empirical for row n: n=1: a(n) = a(n-1) n=2: a(n) = 2*a(n-1) -a(n-3) n=3: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -a(n-5) n=4: [order 15] n=5: [order 30] for n>34 n=6: [order 94] EXAMPLE Some solutions for n=4 k=4 ..0..1..0..1....0..1..0..1....0..1..0..1....0..1..1..0....0..1..1..0 ..1..0..1..0....0..0..1..0....0..1..1..0....1..1..1..0....0..1..1..1 ..0..0..1..0....1..0..1..1....1..1..1..0....1..1..1..0....1..0..1..1 ..0..1..0..1....1..0..1..1....1..1..0..1....0..1..0..1....1..0..1..1 CROSSREFS Column 1 is A000079(n-1) Column 2 is A180762 Row 2 is A001611(n+1) Sequence in context: A159856 A137649 A180915 * A327083 A104002 A073135 Adjacent sequences:  A240780 A240781 A240782 * A240784 A240785 A240786 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Apr 12 2014 STATUS approved

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Last modified May 18 23:41 EDT 2021. Contains 344009 sequences. (Running on oeis4.)