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 A203984 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order 7
 6, 24, 24, 96, 144, 96, 384, 864, 864, 384, 1536, 5184, 7776, 5184, 1536, 6144, 31104, 69984, 69984, 31104, 6144, 24576, 186624, 629856, 956448, 629856, 186624, 24576, 98304, 1119744, 5668704, 13071456, 13071456, 5668704, 1119744, 98304, 393216 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts .....6......24........96.........384..........1536............6144 ....24.....144.......864........5184.........31104..........186624 ....96.....864......7776.......69984........629856.........5668704 ...384....5184.....69984......956448......13071456.......178855776 ..1536...31104....629856....13071456.....271918944......5671161216 ..6144..186624...5668704...178855776....5671161216....180709558848 .24576.1119744..51018336..2447270496..118333620576...5764846339584 .98304.6718464.459165024.33489653472.2469841766784.184042295652096 LINKS R. H. Hardin, Table of n, a(n) for n = 1..220 FORMULA Empirical for column k: k=1: a(n) = 6*4^(n-1) k=2: a(n) = 4*6^n k=3: a(n) = 96*9^(n-1) k=4: a(n) = 15*a(n-1) -270*a(n-3) +324*a(n-4) k=5: a(n) = 25*a(n-1) -45*a(n-2) -963*a(n-3) +2025*a(n-4) +3645*a(n-5) -6561*a(n-6) k=6: (order 15 recurrence) k=7: (order 45 recurrence) EXAMPLE Some solutions for n=4 k=3 ..0..0..0..0....0..0..0..0....0..0..1..1....0..1..0..0....0..1..2..1 ..1..1..1..2....1..2..1..2....1..2..2..0....2..2..2..1....2..1..2..0 ..0..0..0..2....1..2..1..0....0..0..1..1....0..0..0..0....2..0..2..1 ..1..1..1..1....0..2..1..2....1..2..2..0....1..1..1..1....1..1..2..1 ..0..2..2..2....1..2..1..2....1..0..1..1....2..2..2..2....2..0..0..1 CROSSREFS Column 1 is A002023(n-1) Column 2 is A067411(n+1) Sequence in context: A223751 A228745 A049319 * A237836 A231324 A274557 Adjacent sequences:  A203981 A203982 A203983 * A203985 A203986 A203987 KEYWORD nonn,tabl AUTHOR R. H. Hardin Jan 09 2012 STATUS approved

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Last modified September 18 05:51 EDT 2021. Contains 347509 sequences. (Running on oeis4.)